"Eventually, the Christians realized that the Jewish people would not accept their idolatrous beliefs, and decided to introduce their religion to the Gentile world."This is impossible on the surface. How would gentiles have even heard of Jesus if Jewish people had not been believers. This is just another Rabbi rejecting Christianity as they have done for more than 2,000 years.
Christians were Jewish before Christ was born just as Jesus was Jewish in the Messianic Line of David.
And they remained Jewish. The orginal controversy was wether Gentiles could be saved without having to become Jews.