If you read the Book of Acts, the bad blood between Jews who accepted Jesus and those who didn't, started right away. Stephen was Jewish, wasn't he - and he was stoned by the Sanhedrin for professing Christ. Paul, also Jewish, participated in that execution -- and then was targeted for execution himself when he became a follower of Jesus.
Clearly you are right....with much of the Jewish leadership--some of whom had after all pushed for Jesus crucifixion by Rome. Also in Acts it appears, in Judea at least, followers of Jesus were banned from Synagogues.... The apostle Paul though, as late as the 40s and 50s AD, was accepted as a Jewish teacher in synagogues in Asia Minor, however.
The break after the destruction of Jerusalem (at which point arguably, Gentiles out-numbered Jews in following Jesus) was a popular, and pretty final break, not just one of the formal Jewish leadership. I'm talking popular opinion.