I believe that I'm a son of Abraham. Therefore I receive the blessings of YHWH's promise to Abraham. Therefore I'm in the covenant that YHWH made with Abraham.
Fine.
I believe I am a child of God, made so through Christ and his death on the cross. Therefore I am in the New covenant that he came to bring. Therefore I have every spiritual blessing in him, Ephesians 1:3.
That's not what Paul said. Paul said circumcision is keeping the commandments of YHWH.
Galatians 5:2-4
Mark my words! I, Paul, tell you that if you let yourselves be circumcised, Christ will be of no value to you at all. 3 Again I declare to every man who lets himself be circumcised that he is required to obey the whole law. 4 You who are trying to be justified by the law have been alienated from Christ; you have fallen away from grace.
If you read Paul's writings in context; it eliminates the contradiction.
Paul starts his letter to the Galatians by expressing surprise, even hurt, that they should abandon the Gospel that they received from him and accept "another Gospel", Galatians 1:6.
He says that this "Gospel" is no Gospel at all, and says, quite emphatically, that if anyone preaches a Gospel that is contrary to the one that he preached to them, that person should be sent to hell, Galatians 1:8-9.
So evidentially Paul had preached the Good News in Galatia, and they had received it and believed.
What was the Gospel that Paul had preached to them? It was not something that Paul had made up himself, it was revealed to him by God, Galatians 1:11-12. Paul says that the Galatians had heard of his former way of life, in Judaism, when he persecuted the church of God and tried to destroy it, Galatians 1:13. But then God appeared to him, revealed Jesus to him and called him to preach to the Gentiles, Galatians 1:15-16. The story of Saul's conversion is in Acts of the Apostles 9, which also records how he preached that Jesus was the Messiah.
Paul explains in Galatians 2 how he later went to meet with the other apostles. This came about because some false brothers were trying to become part of their group, take away the freedom that they had in Christ and make them slaves, Galatians 2:4. This might be referring to the Council of Jerusalem in Acts of the Apostles 15, which came about because some false teachers were claiming that believers had to be circumcised to be saved, Acts of the Apostles 15:1. If it isn't referring to that, then clearly there was another meeting of believers that met to discuss the same issue.
Paul then spend the rest of his letter talking about faith and the law, and whether keeping the law was part of the Gospel.
In Galatians chapter 3 Paul says that he clearly preached Christ crucified to them, Galatians 3:1 and asks whether they received the Spirit by obeying the law or by believing what he preached, Galatians 3:2? He says that they are foolish and asks if they think that their own human efforts - keeping the law - will save them, Galatians 3:3-5. He then gives the example of Abraham who was considered righteous because he believed. He says that those who observe the law are cursed, Galatians 3:10, that the righteous are those who live by faith, Galatians 3:11, that the law is not based on faith, Galatians 3:12 and that Christ redeemed us from the curse of the law, Galatians 3:13.
Paul then says that God gave a promise to Abraham and his seed, and that seed (singular) is Christ, Galatians 3:15-18. The law was given, he says, because of men's sins UNTIL the Seed, who is Christ, came, Galatians 3:19. Now that faith has come they are no longer under the supervision of the law, Galatians 3:25, but that they are heirs of God through faith in Christ. Christ, Galatians 3:26. Even though they are heirs, he says, they had to be under guardians for a time - for a while they were no better than slaves even though they were heirs. But when the time was right God sent his Son to redeem those who were under the law, Galatians 4:5, so that they could receive the full rights as sons. Paul also says in Romans 8:16-17 that we are children of God and heirs with Christ.
Paul then goes on to give another example in Galatians 4:21-31. He reminds them that Abraham had 2 sons; one by a slave woman and one by a free woman. The son of the slave woman, Ishmael, was born in the "ordinary way" (in fact Abraham got tired of waiting for God to fulfil his promise and decided to do something about it himself). Whereas the child of the free woman, Isaac, was born as a result of God's promise to Abraham and Sarah. Paul says that the Galatians were, and we are, children of the promise. (Read Matthew 1, Jesus was descended from Isaac, not Ishmael.)
Paul begins Galatians 5 by saying that they are free because Christ has set them free and they should not allow themselves to become slaves again, Galatians 5:1. In the Greek manuscripts there were no chapter divisions, so this verse follows straight on from the previous one. Then, Paul says "Mark my words, if you allow yourselves to be circumcised, Christ is of no value to you at all."
THIS is the context of Galatians 5:2 - it follows 4 chapters of Paul saying that those who preach the law as another Gospel are false teachers, that the law does not save and that we are set free from obedience to the law.
He asks them why he is being persecuted if he is still preaching circumcision, says that those agitators should go off and castrate themselves and reminds the Galatians again that they are free, Galatians 5:13. He writes about the fruit of the Spirit - fruit they should bear if they live by the Spirit and the Spirit is in them.
Paul ends chapter 6 by saying that even those who preach circumcision do not keep the whole law; they just want the Galatians to be circumcised so that they can "boast about the flesh"
This over view of Galatians does not lead me to conclude that Galatians 5:2 has been taken out of context - almost his entire letter is saying that they should not believe a false Gospel and put themselves under slavery to the law.
I don't know where John comes into it. I believe John and I believe Paul; I just don't agree with what you are saying.