The New Testament implies many Gentiles were being drawn into Judaism in the first century. The "god-fearers" frequently referred to were Gentiles who knew the Jews were on to something and were strongly attracted to their understanding. Many of the early Christians came from this group, and in many cities, this group outnumbered those who were physical descendants of the Jews.
Also, the Council of Jerusalem (the first church council, where Peter and Paul had it out) was called to settle the question of whether only Gentiles who had previously converted to Judaism could become Christians. In the end, it was decided that Gentiles did not have to become Jews first in order to become Christians.
Paul's attitude toward Timothy's conversion to Judaism (encouraged by Paul) demonstrated that attitudes toward conversion were quite different than today.
Jews in the first century were a theologically diverse group, and included the temple sacrifice-oriented Sadduccees, the ascetic Essenes, the nascent Christians and the "Pharisees", who were the antecedents of what is today considered "Judaism". The separation between the Christians (who at the beginning were almost all Jewish) and the rest of the Jews did not occur all at once,but rather over a period of time, until, in the early 300's, the "Jewish Christians" were ordered to stop celebrating Passover and to abandon the Jewish calendar.
Thanks everyone for the information!