Don't force it when it's religion. Either respect her beliefs enough to find out what it is, for her, or leave her be because she cannot be with you as long as she wants to be faithful to her beliefs and who she is. If you choose to find out more for her sake, or you choose to leave her - both would show respect for her beliefs, because you're not forcing her to do something she feels wrong about.
It's not "just a big fuss" - that religion, whatever it is, is part of who she is. She's simply very very torn over what to do because she seems to like you so very much, yet she feels wrong about getting with you and wants to be faithful to her beliefs, yet the thought of losing you breaks her heart.
Do her a favour - if you really cared about her, either convert to her religion to be with her, OR leave her and accept that you could only be friends. Neither would be wrong of you to do. If she keeps changing her mind when she clearly wants to stick with her religion - that much is clear - then you will have to be the one adamant about not pursuing her, not being too intimate with her, and staying just good friends. Do that because you care so much for her. Otherwise, find out more about her religion to see if it's right for you and if so, convert. Find out about her religion for her sake, if you're willing. Those are the only two options I can really see without her being unfaithful to who she is. And if you feel finding out more about her religion for her sake is being unfaithful to who you are, then leave her be.
In the end, if you two have conflicting views due to religion, the likelihood of clashes when it comes to being in an actual relationship will be much higher, and therefore the likelihood of the relationship working out is also much slimer.
I think I understand how she feels, because I decided not to pursue things further with a major serious crush two years ago because he's agnostic and I'm Christian, and I only date Christians (religious reason). In the end I still got drawn into kissing him etc etc, but I had to finish it in the end because I couldn't bear to be so unfaithful to the God who loves me. You don't have to understand this God part - it was just part of my reasoning and how I felt. And to be quite honest, it hurt an awful lot afterwards but it was the right move, and 2 years down the line I'm now with someone who's Christian and who suits me so well, and looking back I realised that crush wasn't suitable for me anyway. He's a nice guy - but he wasn't good for me personally. But nonetheless you could say I led him on, in a sense, because I couldn't help being drawn to him and wanting to be close to him, and the very idea of not being with him broke my heart that I'd cry night after night after night after night, just crying so hard. She's probably too scared to decide and it hurts too much to not be with you, but at the same time she feels that she has no choice and that she cannot be with you. So yeh, just don't force these things.