I am not sure you can use the word "baptism" like this:
I celebrated my baptism (the fact I was baptized) every year since I was baptized.
I used my baptism (the fact I was baptized) to get close to other Christians to convert them to other religions.
So what do you call the fact you were baptized as a Christian?
Are you celebrating your baptism (the event) or are you celebrating being baptized (a state of being)? For the first sentence I could see either fitting ("I celebrated my baptism..."/"I celebrated being baptized..."). For the second, it makes more sense to say "I used being baptized...", although it also is fine to say "I used the fact I was baptized...".
"Being baptized" is a gerund. You could also use "me being baptized" or "my being baptized" but you don't need to because it's assumed from starting the sentence with "I" (see also When is a gerund supposed to be preceded by a possessive adjective/determiner?).
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")
