Yes.
How are the two mutually exclusive?
If I recall correctly, the early Church born on the day of Pentecost was formed entirely of Jews. Gentile converts came later, after Jesus sent Peter a vision specifically telling him "Go evangelize the Gentiles".
Later, there was controversy in the Church between the Jews and Gentiles, surrounding the question of whether the Gentiles needed to keep the laws of the old Jewish covenant with God. The answering apostle (I think it was also Peter) basically said, "No, and why would you want to burden them with laws even you, a born and bred Jew, were never able to properly uphold?"