(and when Paul went to Jerusalem, these same people were still "zealous for the Law", and took issue with Paul and his Gospel, because his understanding of the Gospel was further developed than theirs was),
That is the new covenant with Israel, that they would have a new heart, and would keep all God's Laws of His covenant with Israel. That was prophesied specifically by both Ezekiel and Jeremiah, and we saw a beginning of fulfillment in the early Jewish Christians. Then the Jews again rejected the Gospel, and God sent it directly to the Gentiles through Paul.
Paul and Peter and James all agreed with each other re the Gospel.
Galatians 2:7-10 KJV
7) But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as the gospel of the circumcision was unto Peter;
8) (For he that wrought effectually in Peter to the apostleship of the circumcision, the same was mighty in me toward the Gentiles:)
9) And when James, Cephas, and John, who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that we should go unto the heathen, and they unto the circumcision.
10) Only they would that we should remember the poor; the same which I also was forward to do.
This was later,
Galatians 2:11-14 KJV
11) But when Peter was come to Antioch, I withstood him to the face, because he was to be blamed.
12) For before that certain came from James, he did eat with the Gentiles: but when they were come, he withdrew and separated himself, fearing them which were of the circumcision.
13) And the other Jews dissembled likewise with him; insomuch that Barnabas also was carried away with their dissimulation.
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?
You assert that Peter had the wrong idea until this correction, however, "For before that certain came from James, he did eat with the Gentiles". Peter didn't seem to have the same problem until these people from James showed up, who were used to keeping the Law.
So, I'm still saying, what we see in the Bible is a one time lapse, and anything beyond that is unsupported.
Much love!