This is actually kind of a tricky one. Your baptism could be considered an event or state of being depending on sentence context. Generally, it'd be an event. So the first example is fine as is. The second sentence technically works but could be seen as confusing language. Your being baptized or baptismal event could be expressed in that circumstance and would probably be better off as...
I used the fact I was baptized to get close to other Christians to convert them to other religions.
Is it longer? Yes. Is it more clear that way? Yes. Sometimes brevity isn't a substitute for precision.
(Side Note: Also, if you're trying to convert Christians to other religions, you're not likely Christian yourself. So "other Christians" should likely be just "Christians")