Find another girl that doesn't blindly follow what she has been led to believe.
or
Wait until she has her own house and then break her away from her religion. (I say own house so her parents don't kick her onto the street or whatever)
No, no, no, no. While I despise religion, if you have to "break" someone out of something like religion that you don't even
really know well at all, like in OP's case, should call the entire thing off, out of respect for that person, because clearly it's lacking as religion is an individual choice. If someone "breaks her away" it should be herself alone. Proselytism of something this nature is selfish, vile, pointless manipulation and completely contradicting to the concept of a relationship.
For the OP, since it sounds like you may be religious too, just a different denomination of Christianity at worst, I have to agree to the simplicity of JAHO. You just never know what will happen until you try. Depending on her age, you might want to be friends with her, get to know her better first (especially see if dating her and being with her is bearable without the usual dating/going-out constraints), and maybe go over and hang out at her house so people (read: family) get to know you --- or you can pop the question and hope for the best reaction. Either way, snoozing is losing, and if this is someone you have a lot of feelings for, you'd likely regret not pursuing them in some fashion.