Converts and perverts

What is the reciprocal term for a religious convert? You could use prepositions, as we do now, to distinguish between a convert from a religion and a convert to a religion. But the rather surprising ninteenth-century term was pervert. To cite a few examples, Levi Siliman Ives, the Episcopal bishop who converted to Catholicism, was described as a “pervert to Rome,” and Rabbi Joseph Krauskopf gave a series of lectures on Jewish Converts, Perverts, and Dissenters. The term was analogous to apostate, but an apostate was someone who left your religion and a pervert was someone who left your religion for something else. The term was understood enough that it could be used without explanation, but it was also controversial enough to warrant discussion. Even more surprising, the religious significance of the term overlapped considerably with pervert used in the sense of a sexual deviant, for which the first example given in the OED appeared in 1856.