Were there "insider movements" in early church?

A recurring theme in missiology is the question of whether a follower of Jesus can remain within the faith community of their birth. These expressions of faith are referred to as "insider movements."

Can a Muslim follow Jesus within Islam? Can a Buddhist follow Jesus as the one who completes Buddhism?

Is there such as thing as "Messianic Muslims" who remain within the mosque, as Jewish believers once remained in the synagogue?

Here's quote from Schnabel that sheds some light on the discussion:

In terms of their message, organization and missionary outreach, the new Christian communities became independent very quickly. As far as we know there was no synagogue in any city between Jerusalem and Rome that became totally "messianic" or Christian, or that tolerated Christian "division."

Why was this so? Were the Christians just obstinate? Yes and no. Schnabel says there were good reasons for the break with Judaism and the refusal to accommodate Gentile paganism.

The Christian faith and practice were the result of the conviction, propagated with energy and courage and the willingness to suffer, that Jesus of Nazareth was the promised Messiah, that he died on the cross for the sins of the world, that he was raised from the dead on their third day, that he was exalted at the right hand of God, and he would return to establish the kingdom of God in a final and visible way.

These convictions . . . constituted a provocation, both for Jews and Gentiles.

Eckhard Schnabel, "Early Christian Mission Jesus and the Twelve" (Eckhard J Schnabel), 550-51.