Is one allowed to study other religions? If not, how is one supposed to know that Judaism is correct? If yes, is such study encouraged?
Mishne Tora, Avoda Zara 2:2 says the study of books on how to worship idols, written by their worshipers, is forbidden. Beyond that I don't know.
The premise here seems to be that one cannot know Judaism is correct except by eliminating other religions. But that can't be, as no one has the time to eliminate every other (existing or possible) religion! Rather, it must be we know Judaism is correct because of internal, as opposed to comparative, reasons.