Me [22M] with my gf [22 F] for 2.5 years. Is it hopeless?

There are two major issues between us, that we've been battling for most of the time we've been together. Everything else is good. We are on the verge of braking up.

1, She has always been a Christian. For the last year she became more active Christian. Started going to church often, helping on gatherings etc.

I've been an atheist since I thought about it. I'm not just used to taking this position, I'm actively trying to challenge it all the time, and I always fail.

I have a problem with this situation, mostly when thinking of having children with her, but also when she takes some decisions that I wouldn't. I've thought about it long and decided that she is such a great person, that is worth making that compromise for her. I really haven't met other such amazing person.

She also has problems with the situation. She thinks it's possible to work for our children, but often doubts it. Because of her beliefs, it's much worse for her. She views is as that I'm going to go to hell, and I might influence our children to follow me. It's not so easy for her to say, everyone decides for himself.

2, She isn't intimately available to me. We often do romantic things, feel really much in love, have fun, etc. But when we get intimate, she often doesn't enjoy it. We used to have sex, but we stopped when she started going to church more. It was really hard for her, when we did. Often felt like it's something bad. Also, from her childhood, she takes intimacy as something evil almost. She doesn't seem to be able to get over it.

I have a problem wit the situation. I'm very sexual and the no-sex has been killing me, but her getting more and more unavailable for even cuddling, makes me feel really bad.

She also has a problem with it, as she feels it's not normal, yet doesn't seem to be able to change it.

Is there hope?

tl;dr: She feels bad that I'm not a Christian. I feel bad that she is intimately unavailable. Is it hopeless?