The old Testament and the relation to Judaism

So, there are many claims around the Bible and the faith, and there are 2 issues always popping up. The first being wether or not the old Testament belongs and relates to the new Testament and the teachings of Christ as well as the relation between Jews, Judaism and the christian faith. 

 

To make it short, the old Testament is correct and accurate. Beyond being historic accounts and lessons taught through those, it also contains records of God building a relationship with humanity, and teaching us the basic things He desires of us. Christ Himself makes constantly quotes and refers to the old scriptures to make His points. He also says clearly

46 If you had believed Moses, you would believe Me, because he wrote about Me. 47But since you do not believe what he wrote, how will you believe what I say?”

And the correctness of the law He also directly affirms

17Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them, but to fulfill them. 18For I tell you truly, until heaven and earth pass away, not a single jot, not a stroke of a pen, will disappear from the Law until everything is accomplished

So what does Paul then mean when he tells us

14For sin shall not be your master, because you are not under law, but under grace.

and 

8For it is by grace you have been saved through faith, and this not from yourselves; it is the gift of God, 9not by works, so that no one can boast.

He means that works can not justify us. The only thing our works earn us is death through our sins. 

23For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.

If the salvation were earned it would no longer be a gift, and as such 

4Now the wages of the worker are not credited as a gift, but as an obligation.

 But God has no obligation to us at all as Elihu rebuked Job 

33Should God repay you on your own terms when you have disavowed His?

Did God not have the right to not create you? Has he not also the right to destroy you without reason? As such works never justify us, but only Gods desire for us to live!

Does this now mean that we can be lazy in our worship? That we can relent from doing what is right? Of course not! Brother Paul in good forsight told us 

24Do you not know that in a race all the runners run, but only one receives the prize? Run in such a way as to take the prize. 25Everyone who competes in the games trains with strict discipline. They do it for a crown that is perishable, but we do it for a crown that is imperishable

In the same way Abraham was offering up Isaac and proofed through this work his complete trust and faith in God, likewise our deeds today testify about our faith as our brother James argued with 

18But someone will say, “You have faith and I have deeds.” Show me your faith without deeds, and I will show you my faith by my deeds

Paul further said

20The law came in so that the trespass would increase; but where sin increased, grace increased all the more, 21so that, just as sin reigned in death, so also grace might reign through righteousness to bring eternal life through Jesus Christ our Lord.

Which again many take as an allowance to sin to enable God to show his grace and mercy is refuted right after by Paul again 

1What then shall we say? Shall we continue in sin so that grace may increase? 2Certainly not! How can we who died to sin live in it any longer? 3Or aren’t you aware that all of us who were baptized into Christ Jesus were baptized into His death? 4We were therefore buried with Him through baptism into death, in order that, just as Christ was raised from the dead through the glory of the Father, we too may walk in newness of life.

 

If we desire companionship with Christ we can not have companionship with sin.

Now how does the "judge not lest you be judged yourself by the same means" fit into that?
Let me ask it from another way around. When God told us 

13If a man lies with a man as with a woman, they have both committed an abomination. They must surely be put to death; their blood is upon them.

Would God now not have an issue with the same act when it was abbominable for Him before? Does this now mean we should put every gay to death? No because remember, even in fair trial we would be condemned to death through our sin, so our sentence must not be just or lawful, but merciful and grounded in love. However you do not watch a loved one stumble blindfolded towards a cliff, you do not let a loved one destroy himself and others around him through the sins. Its better to get a worker of evil to repent and increasing your ranks instead of just reducing the ranks of evil. So a first step would be as Christ said 

15If your brother sins against you,c go and confront him privately. If he listens to you, you have won your brother over. 16But if he will not listen, take one or two others along, so that ‘every matter may be established by the testimony of two or three witnesses.’d 17If he refuses to listen to them, tell it to the church. And if he refuses to listen even to the church, regard him as you would a pagan or a tax collector.

if others are at risk it requires further actions.  

So when we are no longer under the law, it does not mean the law is no longer of importance, but rather its a guideline for what God deems proper conduct, but as any written codex its limited and cant account for every possibility and thus could only cover the basics. As such now that Christ came we are to learn the intentions and will behind the law (instead of jews who know only the letter and weasle their way around the word), and rise above the basics of the law.
As Paul said 

23Before this faith came, we were held in custody under the law, locked up until faith should be revealed. 24So the law became our guardian to lead us to Christ, that we might be justified by faith. 25Now that faith has come, we are no longer under a guardian.

I would also like to point to John Chrysostoms "8 homilies against the jews" where he adresses this issue as follows

(5) We do not say this in accusation of the Law. Heaven forbid! We say it because we wish to show forth the surpassing riches of the grace of Christ. For the Law is not contrary to Christ. How could it be, when he is the one who gave the Law, when the Law leads us to him? But we are forced to say all these things because of the untimely contentiousness of those who do not use the Law as they should. The ones who outrage the Law are those who bid us stand apart from it once and for all and come to Christ, and then tell us to hold fast to it again. The Law has profited our nature very much. I agree to that and would never deny it. But you Judaizers cling to it beyond the proper time and will not let us see how very useful it has been.
(6) It would be the greatest source of praise for a tutor if his young pupil no longer needed him to keep watch over his conduct because the lad had advanced so greater virtue. So, too, it would be the greatest praise for the Law that we no longer had need of its help. For the Law has brought that very thing to pass for us: it has prepared our soul to receive a greater philosophy. 

(7) So it is that he who still sits at the feet of the Law and can see nothing greater than what is written therein derives no great profit from it. But I put the Law aside and ran to the loftier teachings of Christ; yet I could grant to the Law the greatest dignity because it made me such that I could go beyond the trivialities written therein and rise to the loftiness of the teaching which comes to us from Christ.
 

(8) The Law did profit our nature greatly, but only if it led us sincerely to Christ. If this be not the case, it did us harm by depriving us of the greater things because of our close attention to those which are less; it also hurt us by still keeping us in the countless wounds of our transgressions.

Now the Jews argue that God commanded sacrifices, and feasts to be observed, and that Christians forsook the lessons to follow Christs heretical teachings. But do the jews really follow the law? Any Christian should answer here with a resounding "No!". If you have faith in Christ you trust His word, and did He not constantly content with the Pharisee, who are the progenitors of modern Judaism, about how they pay merely lipservice but are hypocrites instead. As adressed earlier, if they had believed Moses, they would have believed Him. Clearly they dont worship our Heavenly Father, for 

23Whoever denies the Son does not have the Father, but whoever confesses the Son has the Father as well.

 Even more, their father, so Christ says, is the devil. 

 Likewise Christ was the ultimate sacrifice, paying every necessary debt, and as such no further sacrifice is required, and with those the feasts also fall away. Now what is left is thanks giving and free will offering you desire to make for God, however the sacrifices are offered in the temple, however that no longer exists so what we have is 

19 Do you not know that your body is a temple of the Holy Spirit who is in you, whom you have received from God? You are not your own;

So the way we sacrifice now is through our body, that is in thought and deed, we sacrifice energy, time, effort, sweat, maybe even blood and our lives, to do what God would desire of us, out of thanks and in love.

But let us adress this in a more objective way
Sacrifices and feasts were commanded to be done at specific times and in specific ways (i.E.: Leviticus 23) on a specific altars in a specific places (Exodus 20: 25-26). While the times may can be observed, and nowadays somewhat the place again, namely Jerusalem, neither the altar, nor the temple is there. Nor is there a legit priesthood present commanded to do the sacrifices (iE: Leviticus 17:5-6). Almost as if God desired to show for all to see that.
It was a very proficient way to take all the things necessary for the observances away so that the only options were accepting Christ as legit continuation of the faith of the prophets, or reject him and remain in their own law, which now eternally condemns them through neglegation of the observances. Jews decided for the later and made up some argument about how God taking everything away from them is not God turning away from them

Also circumcission specifically was the sign of the covenant between Abraham and God

9God also said to Abraham, “You must keep My covenant—you and your descendants in the generations after you. 10This is My covenant with you and your descendants after you, which you are to keep: Every male among you must be circumcised. 11You are to circumcise the flesh of your foreskin, and this will be a sign of the covenant between Me and you. 

Christ was the fulfillment of this covenant, and so taking on the circumcission now (for religious reason) declares that the covenant is still active and that thus Christ didnt fulfilled it and either failed to do so or was illegit from the beginning.

I would also suggest that the law with its specifications, the punishment and severety were fitted to the specific people for that specific time.
In example when we meet Adam, he was given but one law, to not eat of the forbidden fruit.
When we get to Noah he was given a single law as well, to not eat meat with its lifebllod in it.
Why then is the law of Moses so detailed and strict? Because of the people it was adressing. Consider how God led them out of Egypt with the great power and the plagues, yet when the army cam aftter them they start thinking God only wanted to have them die in the wilderness. When Moses went up the mountain to meet God and inquire of Him, the people were already worshipping the golden calve when he returned.

At this time survival was all that matters, they believed the idoltry they and their forefathers engaged in kept them alive and prosper, and so they feared to abstain from their practices. Similary morality was a secondary issue, meaning if the stealing, theft or murder helps you surviving then it would be deemed good by them. So God had to introduce a moral law and make them be more afraid of Gods wrath when not obeying, than they were of dying from neglecting the idols.
Once Gods power and might, and the prosperity of His ways were established He could open and soften up a bit, and bring to us the greater philosophies and intentions behind the law as He did through Christ Jesus.

I would like to end this with a few excepts from John Chrysostoms on the jewish worship

(2) Since there are some who think of the synagogue as a holy place, I must say a few words to them. Why do you reverence that place? Must you not despise it, hold it in abomination, run away from it? They answer that the Law and the books of the prophets are kept there. What is this? Will any place where these books are be a holy place? By no means! This is the reason above all others why I hate the synagogue and abhor it. They have the prophets but not believe them; they read the sacred writings but reject their witness—and this is a mark of men guilty of the greatest outrage.
(3) Tell me this. If you were to see a venerable man, illustrious and renowned, dragged off into a tavern or den of robbers; if you were to see him outraged, beaten, and subjected there to the worst violence, would you have held that tavern or den in high esteem because that great and esteemed man had been inside it while undergoing that violent treatment? I think not. Rather, for this very reason you would have hated and abhorred the place. 

(4) Let that be your judgment about the synagogue, too. For they brought the books of Moses and the prophets along with them into the synagogue, not to honor them but to outrage them with dishonor. When they say that Moses and the prophets knew not Christ and said nothing about his coming, what greater outrage could they do to those holy men than to accuse them of failing to recognize their Master, than to say that those saintly prophets are partners of their impiety? And so it is that we must hate both them and their synagogue all the more because of their offensive treatment of those holy men.

 

Also

I said that the synagogue is no better than a theater and I bring forward a prophet as my witness. Surely the Jews are not more deserving of belief than their prophets. "You had a harlot's brow; you became shameless before all". Where a harlot has set herself up, that place is a brothel. But the synagogue is not only a brothel and a theater; it also is a den of robbers and a lodging for wild beasts. Jeremiah said: "Your house has become for me the den of a hyena". He does not simply say "of wild beast", but "of a filthy wild beast", and again: "I have abandoned my house, I have cast off my inheritance". But when God forsakes a people, what hope of salvation is left? When God forsakes a place, that place becomes the dwelling of demons.
(2) But at any rate the Jews say that they, too, adore God. God forbid that I say that. No Jew adores God! Who say so? The Son of God say so. For he said: "If you were to know my Father, you would also know me. But you neither know me nor do you know my Father". Could I produce a witness more trustworthy than the Son of God?
(3) If, then, the Jews fail to know the Father, if they crucified the Son, if they thrust off the help of the Spirit, who should not make bold to declare plainly that the synagogue is a dwelling of demons? God is not worshipped there. Heaven forbid! From now on it remains a place of idolatry. But still some people pay it honor as a holy place

And further

(3) Nothing is more miserable than those people who never failed to attack their own salvation. When there was need to observe the Law, they trampled it under foot. Now that the Law has ceased to bind, they obstinately strive to observe it. What could be more pitiable that those who provoke God not only by transgressing the Law but also by keeping it? On this account Stephen said: "You stiffnecked and uncircumcised in heart, you always resist the Holy Spirit", not only by transgressing the Law but also by wishing to observe it at the wrong time.

 

Chrysostom further tells us that by offering the sacrifice unlawfully the jews were deemed to be murderers   

Next, in order not to go through each thing individually, he added in summary fashion that it was in no way permitted for them to carry out their customary rituals of worship anywhere else, saying, "Be careful not to offer your burnt-offerings in any place you see; but in the place which the Lord your God chooses for his name to be called, there you shall offer your sacrifices, there you shall perform all that I command you today." For when he said "all," he included, by using this word, festivals and sacrifices and lustrations and purifications and whatever else was in the Law. Then, because they were thoughtless and senseless, and his exhortation was not sufficient to persuade them, he also added an inexorable punishment for those who disobeyed: "The Lord spoke to Moses, saying: Speak to Aaron and to the children of Israel, saying: Anyone from among you, or from among the proselytes / foreigners who are attached to you, whoever slaughters a bull-calf or a sheep or a goat outside the camp or in the camp itself, and does not bring his sacrifice to the doors of the Tent of Witness, blood shall be reckoned for him; that man has shed blood." What does it mean that "blood shall be reckoned for him"? He will be condemned for murder, having become just like a murderer—for [God] was not paying attention to the nature of what was sacrificed, but to the mindset of the one who was sacrificing. For this reason, it was reckoned as murder: because the slaughter took place contrary to God's wishes. Do you see how closely guarded the [issue of] place was? The one who does not sacrifice at the doors of the Tent of Witness, he says, will be punished just as if he has killed a human being, even if he is sacrificing a sheep. And further tightening the punishment, he says, "That soul shall be cut off from his people." Why? Because he did not bring his sacrifices to the doors of the Tent of Witness, he then says. 

as well as

The Psalmist said: "Then Phinehas stood up and propitiated him and the slaughter stopped? He rescued a great many ungodly men from the wrath of God .by slaying a single lawbreaker. This should have happened all the more in your case, if indeed the man you crucified was a transgressor of the Law.
(2) Phinehas, then, was held guiltless after he slew a lawbreaker; indeed, he was honored with the priesthood. But after you crucified an imposter, as you say, who made himself equal to God, you did not receive esteem nor were you held in honor. Instead you suffered a more grievous punishment than you did when you sacrificed your children to idols. Why is this so? Is it not clear even to the dullest minds? You committed outrage on him who saved and rules the world; now you are enduring this great punishment. Is this not the reason?