Who cares what brought on the term. The fact is they were Jews who wanted to hold on to the Old Covenant, and it was true. Paul makes that fact in Galatians 2:11-14, where Paul has to confront Peter's hypocrisy toward Gentiles:
11 But when Cephas came to Antioch, I opposed him to his face, because he stood condemned.
12 For prior to the coming of certain men from James, he used to eat with the Gentiles; but when they came, he began to withdraw and hold himself aloof, fearing the party of the circumcision.
13 The rest of the Jews joined him in hypocrisy, with the result that even Barnabas was carried away by their hypocrisy.
14 But when I saw that they were not straightforward about the truth of the gospel, I said to Cephas in the presence of all, “If you, being a Jew, live like the Gentiles and not like the Jews, how is it that you compel the Gentiles to live like Jews?
The historical context is important because it helps us to understand how the people being talked about in the Bible understood what was being said. If Jesus had said that he came to do away with God's law, then according to Dueteronomy 13, they would have known he was a false prophet, they would have rightfully tried to stone him, and they wouldn't have needed to find false witnesses at his trial, but the crowd had no such reaction. Rather, what he was about to teach was going against the grain of what their religious teachers had taught, so Jesus was assuring them that he came not to end the law, but to correctly interpret it.
In the same way, Judaizers had nothing in particular to do with the Old Covenant, but rather they were wanting Gentiles to become Jews and follow their traditions in order to be saved. Up until Peter's vision in Acts 10 the only Gentiles who had been saved were those who had become Jewish proselytes according to their traditions, so while their position was wrong, it was nevertheless understandable. The objection to Judaizers was not that they wanted Gentiles to obey God, but that they wanted Gentiles to obey God according to their traditions in order to be saved. Obedience to God's law is the way to identify with God, not the way to identify with Jews.
The Jews had man-made traditions that forbade them from visiting or associating or visiting with Gentiles (Acts 10:28), so when Peter gave heed to their traditions by changing where he was eating, he was giving credence to their position that their traditions needed to be followed, and his actions were essentially telling Gentiles that they weren't actually saved, which is why immediately reiterated in verse 15 that we are saved by faith. Living like a Jews again refers to keeping rabbinic traditions.
How you can read the book of Acts, knowing the Jews were so angry with Paul teaching New Covenant salvation in Christ, the swore an oath to kill him in Acts 23:12, because Paul's preaching was converting Gentiles. They followed Paul everywhere, yet here you are trying to change the facts.
Abraham was saved by faith, just as we are, and just as everyone else who has ever been saved, so the way to become saved didn't change between covenants. Salvation is from sin, and sin is defined as the transgression of the law, so our salvation is from transgressing the law, which necessarily involves coming into to it as we are made to be more like Christ in following his example of obedience. They wanted to kill him because of false rumors that he was teaching against the law, which he denied in court.
What is Paul's warning to the Philippians about them? Philippians 3:
2 Beware of the dogs, beware of the evil workers, beware of the false circumcision;
3 for we are the true circumcision, who worship in the Spirit of God and glory in Christ Jesus and put no confidence in the flesh,
The false "circumsion" are Jews who wanted to make Gentiles obey the Old Covenant!
Circumcision that is done for the purpose of justification is just mutilation of the flesh, that was never why circumcision was commanded in the first place.
Who argues that point?? We understand that living in obedience to Christ is what we ought to do! What you don't forget is that even when you have done all that you're supposed to do, what are you to say? Did you miss Luke 17:10?:
10: "So you too, when you do all the things which are commanded you, say, 'We are unworthy slaves; we have done only that which we ought to have done.'"
Jesus was not in disagreement with the Father about what we ought to do, but rather he said that he came to do only the Father's will and that his teachings were not his own, but that of the Father (John 7:16). He taught to obey the law both by words and by giving us a perfectly sinless example to follow, so I am in complete agreement that we ought to obey Christ and not in order to become worthy of anything.
This is pure imagination. There was no "exhuastive list" except that which the Jewish Rabbis created thinking the could be righteous by doing so. This is the very thing Jesus spoke against them about. Have you read Matthew 23? They had made the Law a burden to the people adding to it...so get it straight. The apostles understand that WE WALK IN THE SPIRIT...and they command us to do that instead of obeying the Law.
If you agree that it is not an exhaustive list, then it should also include God's laws. The role of the Spirit is to lead is in obedience to the law (Ezekiel 36:26-27), and the Spirit is not in disagreement with the Father about what conduct we should have, so walking in the Spirit precisely is walking in obedience to the law.
I think you need to read that passage carefully...you're just wrong about that. Paul wasn't keeping the Law, as much as he was appeasing the Jewish believers. Don't get me wrong, I know there are Jews even today that are Christians that still observe the Sabbath under the Old Covenant. That's no problem for me...EXCEPT, when they try get me to do so. I'm free in Christ and I will not try to be righteous by their standard.
However, let's let Paul explain to you why He did those things. Have you ever read 1 Corinthians 9:19-23?:
19 For though I am free from all men, I have made myself a slave to all, so that I may win more.
20 To the Jews I became as a Jew, so that I might win Jews; to those who are under the Law, as under the Law though not being myself under the Law, so that I might win those who are under the Law;
21 to those who are without law, as without law, though not being without the law of God but under the law of Christ, so that I might win those who are without law.
22 To the weak I became weak, that I might win the weak; I have become all things to all men, so that I may by all means save some.
23 I do all things for the sake of the gospel, so that I may become a fellow partaker of it.
Paul never got it confused!
Acts 6:13 and they set up
false witnesses who said, “This man never ceases to speak words against this holy place and the law,
Stephen was falsely accused for teaching against the law, so the straightforward interpretation is that there were also false rumors that Paul was teaching against the law and they wanted to disprove those rumors and show that Paul continued to live in obedience to the law because that's what he was doing. Paul said that he upheld the law (Romans 3:31), that the law is holy, righteous, and good (Romans 7:12), that he took delight in God's law (Romans 7:22), and that the law tells us what sin is (Romans 7:7), so it is also straightforward continued to keep God's law because he thought it was a good idea to obey Him and to avoid sin. That is unless you'd prefer to go with the convoluted interpretation that maligns Paul's character and makes him out to be a super secret double agent, who tells different groups different things, which would make him out to be the ultimate hypocrite because that's exactly what he called Peter out for doing. Paul was not suggesting that we should sin in order to reach sinners because that would undermine the very message that he was sent to preach, but rather he spent the chapter talking about giving up his rights and not holding himself above others in order to reach more for Christ. Note that in verse 21, he specifically said that he was outside of God's law. When everything Paul said and did supports my position, but you need to say that Paul secretly held your position and no one called him on it even when he publicly admitted that's what he was doing, then it's time to reconsider your position.
I think you've got it a bit misconstrued. We identify with God, through the finished work of Christ on the cross, and it should not be translated "works of the Law". It should be translated as it says JUSTIFIED BY FAITH!!!
Here's a link to help you the the Greek of the text using Romans 5:1, which says:
Therefore, having been justified by faith, we have peace with God through our Lord Jesus Christ,
Christ died on the cross to free us from sin, which is the transgression of the law, so we have been set free to not transgress the law. By obeying the law, we are identifying with Christ and the example that he set for us to follow. The law was never given as a means for how to become justified, but as instructions for how God wants those who have been justified to live. If Moses was justified, then he was justified by faith before the law was given to him, so the law is God's instructions for how the righteous shall live by faith, not how to become righteous.
The link is from Blue Letter Bible:
https://www.blueletterbible.org/nasb/rom/5/1/t_conc_1051001
You're mixing law and grace...PERIOD!
That's good because the Bible also mixes law and grace:
John 1:16-17 For from his fullness we have all received, grace upon grace.[d] 17 For the law was given through Moses; grace and truth came through Jesus Christ.
Romans 1:5 through whom we have received grace and apostleship to bring about the obedience of faith for the sake of his name among all the nations,
It says grace was added to grace, so the grace of Christ was added to the grace of the law and the grace that we have received is to bring about obedience of faith to the law.