The Big Split - the Jewish Tax
After the fall of Jerusalem in 70 C.E. the Romans had essentially conquered the Jews. Yet they knew from past experience that the Jews would not renounce their faith and integrate into Roman paganism. But it had cost Rome a lot of money to wage war on the Jews, and they needed to replenish the treasury. So Rome enacted a tax on all Jews, the fiscus judaicus or Jewish tax.
During the decades of the 70s and the 80s this tax was collected very aggressively. Anyone with any connection to Judaism could be hit, those who had renounced their religion and tried to keep their Jewishness a secret, as well as those who made no claim to Jewish heritage but lived according to Jewish customs. This must have made many Gentile believers rather irate, to have to pay a stiff tax aimed at Jews when they were not Jewish.
In 96 C.E. Nerva succeeded Domitian and clarified and relaxed the tax. The only ones liable to it would be those who "followed their ancestral customs". This meant that there was an opportunity to avoid paying the tax by abandoning the Jewish way of life. For most religious Jews, whether Jesus-believing or not, renouncing their Judaism would be unconscionable. But for Gentile believers who didn't have the deep background in Torah and may have seen their connection to the despised Judaism as rather tenuous, the temptation would have been great. If they could redefine their relation to God to exclude Jewish practice, they could avoid a lot of financial hardship.
There were ample opportunities in the New Testament to build such anti-Jewish traditions. Galatians and parts of other epistles, when interpreted in a certain manner, certainly distinguished Gentile believers from Jews and appeared to discourage Torah observance. So these kinds of traditions developed rather rapidly.
It is interesting that at this same time the Gentile leaders in the church began to greatly minimize their reliance on the Hebrew Scriptures in their writings. If we compare early writers such as Clement to later writers like Polycarp, we can see how dramatically the source of authority changed from the Tanakh to the apostolic writings in just a few short years.
The Big Split - Three-Way Split