The situation you're in must stink.
In any on and off again relationship, I recommend really taking the time to evaluate if this is something you really want to pursue.
She's probably very conflicted internally about her feelings and about your relationship. And she probably needs time to sort out what's important. That's the ENFP's Fi at work.
As an ENFP, I find that I'm usually pretty open-minded about all sorts of things. Other ENFPs I've met have the same tendency. Maybe she's moving towards that.
She might also be having a conflict with her inferior Si. Hopefully, she hasn't fallen into the grips of it though.
If she turns out to be like me, she'll eventually find a way to connect her religious beliefs with what she feels and really thinks. It's possible for everyone. For me, it was a matter of realizing that I was taught that the religion I was raised in (rather conservative evangelical Christianity, which is strange because my parents are as religiously moderate as they come) was all about love and acceptance and being a better person. Not about hating LGBTQ people or shoving religion into the government and onto people who might not share it or rigidly enforcing gender norms. For me it was questions like: How am I supposed to believe my transgender friend is wrong and sinful just for being true to himself? That caused me to reevaluate. I'm also not even heterosexual myself, that was a big part of it too. There was also a crap ton of hypocrisy.
So I stopped listening to the religious right and got out of the conservative religious educational program that my parents were told would be good for my anxiety by some well-intentioned friends. Graduated from public high school, and now I'm enrolled in a secular, liberal arts university. I hope to either earn a Master's or a PhD. My education has taught me critical thinking skills that I was denied in the religious based program. While everyone was kind to me, I learned that my Ne made a lot of people uncomfortable so I learned to conceal it or only show it when it would be deemed acceptable. It's not good for an Ne-dom such as myself to do all the time, but it has been a useful skill that has allowed me to make friends with all sorts of people.
Sadly, this took a few years. And I'm thankful that neither myself nor my parents were too deeply entrenched into what I see is a corrupted way of thinking about my religion in particular.
Religious matters are tricky though. Once some people hear that God has said something, they take it verbatim and won't change their perspective ever. But it can change. I've seen a rather conservative ESFJ abandon the idea that being attracted to the same gender is a sin.
And then there's my ISFJ friend who is really a lovely person. She just has some transphobic tendencies. She's not outright hateful. She treats everyone with respect and doesn't talk much actually, but there is some ingrained transphobia. You can tell how frustrated she gets when someone contradicts anything she thinks or questions her in-depth. I have made a point not to introduce her to my extremely liberal ESFP friend who carries around a lipstick case that says "F*** Trump" (proceeds went to Planned Parenthood) and an even bigger point not to introduce her to my transgender ISTJ friend. It's possible that she'd get along very well with both, but if any social issues come up (feminism and a women's right to choose with the ESFP and LGBTQ issues with the ISTJ)- the ISFJ will get frustrated and anxious, the ESFP and ISTJ might flip out, and I'll probably get upset because if I think my friends should be able to get along with my other friends. Then again, I'm friends with all sorts of people. I suppose then certain combos like that are inevitable.