I don't necessarily agree with Carrier on that. I think most people, including him, have read way too much into a lot of the later harmonization and reconciliation that took place.
I see most all of this as emanating out of Ephesus, Paul's base of operations, and likely were Paul's letter collection was started, where the Gospel of Mark was written, Marcion's Gospel was written, and the Gospel of John was written. Nearby is where Revelation was written.
I think there is a lot of confusion over what the "Jerusalem church" was and what those people had to do with Paul or Jesus. Still too much dependence on Acts, which situations everything as coming out of Jerusalem. But that's second century propaganda.
There is an assumption that "Jesus" was the central issue. I don't think that was the case.
We know precious little about Peter or about what the issue was that Paul discussed with the Jerusalem church. The issue appears to have been circumcision. I also think, BTW, that Gal 2:8 is a later interpolation: 8 "(for He who was at work for Peter in his apostleship to the circumcised was at work for me also to the Gentiles)" I see this as a later addition intended to refute Marcion's claim that Paul was the only apostle to whom Jesus was revealed. This adds Peter to the list. 1 Cor 15 5-11 is also an interpolation for the same reason.
The issue was that Paul was converting people without circumcising them. He went to the Jerusalem church to get approval of his conversions without circumcision.
Did the Jerusalem church even care about "Jesus Christ"? We don't actually know. People assume so, but that's a bad assumption based on later literary developments.
1 Corinthians is really the only thing that tells us that Peter had anything to do with Christ, and even then it takes some inference. There is indeed nothing that ties any other apostle to "Jesus", only to "Christ" or "the Lord". But did those people associate "the Lord" with Jesus? We can only assume.
Quite obviously, many Jews would have worshiped "the Lord" or even "the Messiah". Who named the Lord Jesus aside from Paul? We have no idea. My point is that there are a lot of loaded assumptions that go into most people's assessment of what was going on, including Carrier's.
We have no idea if Peter or James or Apollos taught that "the Lord" had been crucified, or "Jesus", if they equated "the Lord" to "Jesus" how they conceived of "the Lord" or Christ or Jesus, etc.
Paul's language about the Lord, Christ, and Jesus is pretty specific and also pretty unique. In my reckoning, virtually every work of the NT ultimately derives from Paul, all borrowing his language, etc. How broadly shared that language actually was outside of Paul is not really known. We don't even know if Paul's account of the Jerusalem meeting is legit. He was trying to impress upon the Galatians that his teachings had been approved, and then tells that Peter was a hypocrite. This is his explanation for why it seemed that his teachings had NOT actually been approved and weren't supported by others.
So Paul is claiming that he met with the leaders of the Jerusalem church and that they agreed with his teachings, but apparently the Galatians had heard otherwise. There is no evidence in my mind showing that the "Jerusalem church" knew anything about Jesus at all. Maybe they did, maybe they didn't.
James and Cephas and John, who were reputed to be pillars, gave to me and Barnabas the right hand of fellowship, so that we might go to the Gentiles, and they to the circumcised. They only asked us to remember the poor—the very thing I also was eager to do.
We really have no idea what the common theological framework was between these figures. Did they all distinguish between "God" and "the Lord"? Was the common framework a belief in the coming End of Days? What was the purpose of Peter's ministry to the circumcised? People assume that it was to tell them about Jesus, but this is quite doubtful. It seems to have involved baptism. It seems that the main objective of the ministry would be to get donations for the poor, as Paul repeatedly outlines, and to baptize people to prepare them for the coming of the Lord. What the "coming of the Lord" meant to Peter, James and John I cannot say, but preparation for the "coming of the Lord" would not have been out of place or unusual among Jews at this time. It certainly didn't require any association with "Jesus" -- the coming Lord Yahweh would be assumed.
So, in my mind, its quite possible that the "Jerusalem church" merely sought to #1) help the poor, #2) were preparing for the "coming of the Lord" (whatever that meant), and #3) might have been a group of Jews who saw a distinction between "God" and "the Lord", seeing "God" as the universal Creator and "the Lord" as Yahweh of the Jews. Maybe they also identified "Jesus" with "the Lord" or "the Suffering Servant", but I don't find that necessary given information we have.