Bernard Muller wrote:When these Galileans got in control of the remnant of the church of Jerusalem after the Greek dispersion, their influence was very limited because they were not Christians.
I think it is very unlikely that the Jerusalem church did not believe in the resurrection of Jesus Christ (my criteria for being a Christian).
In Galatians Paul implies that Jerusalem has a group of people who are “reputed” (Gal 2:6, 9). Included in this group are James, Cephas and John who Paul informed about the gospel he was preaching (Gal 2:2) and this group gave to Paul “the right hand of fellowship” (Gal 2:9) and in return they wanted Paul and those he coverts to remember the poor in Jerusalem. He also calls them apostles – “nor did I go up to Jerusalem to those who were apostles before me” (Gal 1:17a). Paul bases his authority on being an apostle and he often uses that title when he introduces himself – Rom 1:1, 1 Cor 1:1, 2 Cor 1:1, and Gal 1:1.
Paul refers to “the collection for the saints (or holy-ones)" (1 Cor 16:1) and it will be carried to Jerusalem (1 Cor 16:3) and “I am going to Jerusalem to assist the saints … some contribution for the poor among the saints at Jerusalem;” (Rom. 15:25) before going to Spain via Rome. Paul usually uses the term “αγιοι” (saints or holy-ones) for other Christians – Rom. 1.7, 1 Cor 1:2, Eph. 1:1 – “To all the saints who are present and believing in Christ Jesus”. Paul states there is no difference between those converted by Cephas, or Apollos or himself – ‘"I belong to Paul," or "I belong to Apol'los," or "I belong to Cephas," or "I belong to Christ." Is Christ divided?’ (1 Cor 1:12b-13a) to which the answer is no ‘you are Christ’s’ (1 Cor 3:23a).
When Paul has a disagreement with Peter and James at Antioch it is not about belief in the resurrected Jesus Christ, it is only about Gentiles living under the Torah (Gal 2:11-21).
Therefore from Paul’s letters it is clear that Paul had no dispute with the Jerusalem leadership regarding Paul’s preaching of Jesus Christ resurrected. That he considered the leadership equal with other groups of Christians and himself. That he recognised that they had a special place in the movement and that he should get other churches to provide support for the Jerusalem church. And that he considered that those people converted by Peter as being the same as those he converted. It is very unlikely therefore that the Jerusalem church had a completely difference message about Jesus than Paul.