The disputes do go back farther than that, to the late 1st century C.E. After the destruction of the second temple at the hands of the Romans in 70 C.E., Jews were upset that the Nazarene sect had not assisted in the resistance. Further, by the 90's the theological divide was becoming more marked. Nazarenes were upset that the Jews were not accepting Jesus as the messiah, and the idea that he would be returning. Jews were alarmed at the evolving Christology of the Nazarenes, which was turning Jesus from a rabbi and messianic claimant into a godlike figure. By the 90s C.E., Christians were no longer welcome in the synagogues, and Jews were subject to greater criticism in Christian writings.
This animosity did not last permanently, though. At the time John Chrysostom became bishop of Antioch, he was horrified to find Jews and Christians living in fellowship, and began his campaign against the "Judaizers". This continued into the councils of the 4th century, and became the official position of the church.
From what I gather, you believe that the Messiah Jesus evolved from the Rabbi Jesus. That is his divinity was made up after the fact?
Wasn't it mainly the Zealots who were "upset that the Nazarene sect had not assisted in the resistance"?
The Zealots were upset (to put it mildly) with more than just the Nazarenes -- Johanan ben Zakkai and his group (Pharisees?) were also targeted, for example.
So as far as I know (and I admit I don't know much), early relations between Nazarenes and other Jewish groups weren't especially strained, with perhaps the exception of the Zealots.