Just so we’re all on the same playing field, I’m an Atheist.
I don’t care about the source of my imaginary SO’s beliefs, ideas, attitudes, etc. I just care about what the beliefs, ideas, attitudes, etc. are.
If she believes that homosexuals shouldn’t have equal rights (Marriage, or otherwise), I would lose interest in her. Whether she’s come up with that idea from her holy book, or from her parents, or from just her own brain, that doesn’t matter. The fact that she believes it is what matters.
So the likelihood of me getting really involved with a religious girl? VERY VERY VERY unlikely, considering the sheer amount of disagreements I have with popular religions.
That said, my best friend growing up was a Christian (I know he went to a presbyterian church, not sure what exactly his beliefs are). Whenever we started to talk about religious things, we had arguments. But the next day we’d get together to play some video games. Because our religious beliefs had nothing to do with our interest in video games.