Q. Is one allowed to study other religions for the sole purpose of being able to be mekarev and bring back the ones that fell and converted to them?
A. Rambam (Avoda Zara 2: 2) mentions that "many books were written by idolaters to explain the ways of serving their deities, and Hashem prohibited studying them." However, on the next chapter (3: 2) he rules that Beis Din has to know the ways of the (avoda zara) service, since they would not be able to punish the transgressors, unless they know that it was actually served. Rambam repeats this ruling in H. Sanhedrin (2: 1) "The judges have to understand the emptiness of avoda zara, so they can stand and judge the transgressors."
The above is based on the teaching of the Talmud: (Sanhedrin 68a and Sifrei - Devarim 18: 9) "When you have come to the land Hashem... is giving you, you shall not learn to do like the abominations of those nations." meaning that, to do is prohibited, but to learn to understand how degenerate their actions are, and to teach your children, “Do not do such and such, because this is a heathen custom!" is permitted. (Rashi ibid.)
Similarly, Rambam writes that he extensively read all books on these topics, and from them he understood the reasons of mitzvos (Kovetz Tshuvos HoRambam - Igorois to the Sages of Marseille p. 25, See More Nebuchim 3: 29).
Igrois Moshe (Y.D. 2: 53) permits the learning and teaching of ancient religions, when stressing and explaining the fallacies and misconceptions inherent in them. He further explains (Y.D. 2: 110) that studying books of other religions that contain persuasive material, is only permitted to Gedolei Hador in Torah and Heavenly fear, but not to ordinary people, unless they have been properly prepared and edited.
The well researched sefarim and educational material, written by Rabbi Aryeh Kaplan (The Real Messiah, etc.), Rabbi Michael Skobac (Jews for Judaism - Missionary Impossible, The DaVinci Code), Rabbi Bentzion Kravitz (The Jewish Response to Missionaries) and others, are great examples of the above rulings.
See also questions 1963 and 1964 in regards to learning Greek philosophy.
Horav Shlomo Miller's shlit'a opinion is that it is permitted only when the information learned will be used in proper kiruv need, the reader is well trained and properly prepared and when the idolatry is also ridiculed and disrespected.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a