First, let's address why Jews would convert to Christianity. Some did so to escape the oppressive taxation meted out by governments who used Jews as their purse because Jews were so often money-lenders. Another reason might be the opportunity to advance a political or professional career in fields where the Christian (or Islamic) authorities would not hire Jews. They might have wanted to get out of the ghetto, the place to which Jews were restricted, instead of living in the nicer parts of the city. And let's not omit the possibility of a real change of faith and acceptance of Christianity.
How were conversions received by those who "stayed behind"?
Rabbinic authorities debated whether those who converted were traitors to the faith or victims. Many conversions were victims, because they were coerced under threat of death. Forced baptisms also took place. This could lead to Marranos, so-called "crypto-Jews": individuals who lived publicly as Christians but secretly kept Jewish practices at home. The Spanish Inquisition went after Marranos and Moriscos (converted Muslims) with severe penalties for any who were not fully embracing Christianity and abandoning all facets of their former faith.
Sometimes agreeing to conversion to avoid death did not work because the Christians offering "salvation" were out for blood anyway. Parents would kill children and then themselves in order to avoid forced conversion.
The apostate who turned from Judaism to Christianity was in a strange state of being neither fish nor fowl. Former fellow Jews rejected him, and Christians still looked at him askance. If he wished to return to Judaism, his former neighbors still might feel awkward, but official rabbinical attitudes were different.
The rabbinic scholar Rashi (1040 - 1105; mentioned here) claimed a Jew remains a Jew regardless. A Jew who fell away from the faith could simply return to Jewish practices and be fine. Another, Gershom ben Judah (c.960 - 1040), forbade mistreating an apostate who returned to Judaism or even mentioning their past choices. This was different from Christian and Muslim attitudes toward those who left those faiths.
Rashi's pronouncements were so respected that he became legendary. Seriously: legends arose about him, even miracles performed while he was in the womb. Let's meet him next time.
