This is off this post but you asked me what gospel was referred to in Galatians 2:14. I have done some study and I will convey what I know at this time.
[Gal 2:11 KJV] 11 But when Peter was come to Antioch, I withstood him to the face, because he was to be blamed.
Peter came to the church at Antioch where Paul withstood him
[Gal 2:13 KJV] 13 And the other Jews dissembled likewise with him; insomuch that Barnabas also was carried away with their dissimulation.
There were Jews in the church who more than likely believed Paul's gospel and were influenced by Peter
[Gal 2:14 KJV] 14 But when I saw that they walked not uprightly according to the truth of the gospel, I said unto Peter before [them] all, If thou, being a Jew, livest after the manner of Gentiles, and not as do the Jews, why compellest thou the Gentiles to live as do the Jews?
Who are the "they" who walked not according to the truth of the gospel? The Jews who believed Paul's gospel and were going after Peter in separating from the Gentiles instead of knowing there is no Jew or Gentile in the body of Christ.
LOL! Nope, Peter and Paul preached the same Gospel, thus Paul was able to call Peter out for not walking according to THE (one) truth of THE (one) Gospel--they both agreed about the same regulations they were held to walk according to, thus Peter was able to humbly receive the correction Paul brought.
The reality is that, as we see with Peter, there is an ultimate truth that is true in the Gospel, but there is also the person's personal conscience that is true--and the person is not permitted to cross the boundary of their personal conviction for the sake of the ultimate truth. They may not be there yet, and that is OK. One example is the vegan who believes (and this is the example given in Ro 14)--he is
actually sinning if he goes against his conscience, irrespective the higher, ultimate, reality of the Gospel that it is OK to eat meat, because he is not "there", yet, in his conscience, not able to conform to the actual truth that is true in the Gospel. The same goes with someone who is not there yet with eating food sacrificed to idols--Paul says it's fine, but it is a sin to cause one of these little ones who believes in Jesus to stumble by becoming an occasion for them to injure their conscience.
God calls us to peace--and going against your conscience threatens to destabilize one's peace.
This is also seen with Peter--though it was a truth in the Gospel that he was not under the Law, he says, "Not so, Lord, for nothing unclean has ever touched my lips" when the Lord said "rise kill and eat [unclean food]", and, so, we see that he was walking according to his Torah-informed conscience, and he was actually held to his conscience, just as the vegan, just as the one who is accustomed to the idol (who cannot eat idol-sacrificed food), BUT, in due time, the Spirit of Truth led him in to all the truth, revealing to him, in a vision, the actual truth of the Gospel that he was not under the Law anymore.
(Peter didn't have the vocabulary for it, didn't know the next steps of the dance, but, nevertheless, he was under the selfsame Gospel as Paul--Paul, however, having been more acquainted with the Scriptures, had the vocabulary for it, with the help of the Spirit of Grace. It was his calling, God having formed him for that purpose, to help others, to dispense God's grace, giving the audience their food, milk or meat, in due time.)
This dynamic of the truth is exemplified in Ro 14, where Paul tells the believing Jewish and Gentile audience that there is a single Law for both the native (Jew) and the sojourner (Gentile) : each man must be fully convinced in his own mind. The Jew who observes a day observes it in full persuasion as unto the Lord, and the Gentile who does not observe the day does not observe it in full persuasion as unto the Lord--and both are accepted because they are walking in full persuasion (but "what ever is not of faith is sin" with the result that the sinning Christian "is condemned" Ro 14:23), irrespective whether it aligns with the ultimate truth of the Gospel, which God will eventually lead them into as long as they keep consistent and their consciences clean.
This again explains Peter's acceptability irrespective his not having known or walked in the ultimate truth of the Gospel that he was not under Law... until the vision was given to him... releasing him from the weakness of the ignorance that he had been bound to (even before God, he was bound to keep those things, because it was his conscience).
This was why I'd asked whether you, with your "remnant of Israel Church" and "body of Christ Church" dividing, had been trying to solve the issue of the Jews' seemingly having been under Law in Acts 21--if you want, I have answers for that, as well.