This is simply not true.
Earlier, Peter had a vision from God that indicated that henceforth Gentiles were not to be considered “unclean”–unclean in as much as Christian Judaism was now to [formally] welcome gentile converts. (there had always been ‘proseltytes’ that were non-Jews who were accepted within the Israelite nation and given respect. They were not a formal part of the Jewish religious establishment, and not given the same rights/accord as Jews)
By the time the dispute in Acts 15 took place, the decision to accept gentiles had been made and was moving forward. However, now that gentile converts were streaming in, questions/disputes arose. Among some, the new converts had to be circumcized according to the Mosaic Law, a law that they had lived with* for centuries.*
No one in that dispute grappled with the notion that ’ they were a separate belief system.’ With all due respect, this suggests you don’t understand the continuum. Both he Jews who accepted Christ, and those who did not, were waiting for the exact same thing: the arrival of the Messiah, something thaey had waited for for centuries. The apostles and the other followers saw Jesus Christ as the long awaited Messiah----while the majority of the Jews did not. Ultimately that majority had Christ killed as a seditionist.
But all of them—Christian Jews and non-Christian Jews—were convinced that they were practicing ‘correct’ Judaism.
The dispute had everthing to do with what role, if any, the Mosaic Law should/would have now that the Christ had come, and that resolution applied to Christian Jews and Christian Gentiles alike.
(The issue of circumcision brought this to a head (no pun intended) but we’re not talking about cirumcision as much as we’re talking about the ending of the whole Mosaic Law—a group of laws that numbered somewhere around 600 laws. The ending of the requirement of circumcision would have applied to Jews and Gentiles alike. (Jewish males were circumcised as infants) Further, hundreds of other ceremonial laws would be ended along with circumcision, like mixed threads, shellfish etc etc etc)
Paul arbitrated and made a forceful argumant that the Mosaic Law died when Christ died, and they were now under a new covenant–rather than the Law of Moses, Christian Jews (& Gentile converts) were now under the Law of the Christ.
Among those who insited that the gentile converts be circumcized, they weren’t asking for them to become Jews, (an impossibility) but rather insisting that the converts be subject to Jewish Law–the Mosaic Law.
But there is nothing to suggest that they were contemplating a “different belief system.” They were Jews, follwing what they considered to be Judaism.