I dated a woman who did similar (just minus the distance). It didn't go well at all because Jesus was everything to her. The picture you paint of your lady sounds similar. She has already given you enough info that you will not be equal unless you let Jesus into your heart. She may say she is not judging you, but she is. It is like the "stop hitting yourself" thing kids do. Time to run if it was me.

If it's already causing a problem, I would get out while the getting is good.

To use their term: unequals don't work together, especially in a supposedly loving relationship. That's been my personal experience and observation. My last girlfriend was nice enough at first, then religion crept up, it came out in her more and more. I tried not to argue with her or even bring the subject up, but it's an obsession with them. She talked to herself a lot, quoting stuff from the bible... fing nutty. We lived together but I had to sleep in another room and I eventually moved out. We ended with her rebuking me, insisting I had demons swirling around me. I don't care if they seem relatively rational on the outside, inside they're a sticky, nutty mess. Forget about it.

I would ask yourself, "Do I feel safe with her? Can I truly be myself around her? Do I feel the need to hide parts of myself? These questions may help you gain clarity that you need.

Give it a try.

Well, anyone that knows me will know I'm agnostic and I don't believe in God. So, religious or not, has to respect that. That shouldn't be an issue whatsoever. That's in theory. In practice, a couple must know how to deal with the differences between each other. I never experienced that but I wouldn't let be an issue by being straight from the very start.

Well, you could turn the tables on her. Tell her that if what she is saying is true, she should be able to prove to you that there is a god. By doing that, and doing so all in direct sincerity, it puts the ball in her court, and, obviously, she will fail. She may drag your ass to church, but if you are willing to push the issue and strong enough to weather the social pressure, and, able to directly not only par her arguments but also reveal why you are an agnostic, you may turn the tables on her. This is clearly a strategy that is explosive and dangerous to the relationship, but, given the current situation, I don't see a whole lot of hope for it as it stands . . . . if you let her continue on the same route, the shit is going to hit the fan anyway, so turning the tables on her is probably your only hope. By the way, when you deal with people like this, they will try to tangentialize the argument . . . in this case, what you will see is she will try to stray from the proving, change the argument, and you have to force the argument to stay on PROOF of god's existence, if you let her change it, it will destroy your success in turning the tables on her . . . . she has to prove it to you, and, listen to your counter-arguments.

You will hear people who tell you that it is impossible to change their mind, but it is not. I know, because I changed my mind after a discussion with a German fellow with whom I am eternally grateful for . . . . the key is, people think that others should change their mind right then and there, during the discussion, and it does not work that way . . . . it happens afterward, when they start thinking about how they are going to rationalize their belief, and how they are going to counter the argument, and realize that they simply can't!

Also, my bet is that if you dig deep enough, you will find that she is either wanting to get out of the relationship anyway, or, the more likely scenario, she is being pressured by her fellow believers to conform by forcing you to conform.

I have a similar situation
I have a friend in NY whom I have become very close to recently who is Christian. He's a lovely kind hearted person but does too much preaching to me, even reading his devotionals to me. I find it rather annoying. He thinks he can bring me back to the faith because I'm rather well versed in ancient texts. He doesn't understand that I will never be evangelized. It's tough because I really like him otherwise.

Ask her to join the church of England. She will soon get bored with the whole idea.