It's hard to be yourselves in the relationship. Your values just don't match up, and that extends to your deepest beliefs on a spiritual level. You try to talk about the things that are important to you, but you find that your ideals are not in the same ballpark at all.
If the relationship is important to you, your partner, especially, might start trying to cover up their beliefs -- denying their ideals in an effort to save the relationship. But there's no reason why clashing values or spiritual beliefs have to mean the end of an otherwise perfectly good romantic connection. Sometimes, the tension and stress created by an aspect like this one is enough to kill the relationship, but you could also choose to learn from it, and from each other. This takes a conscious commitment on both your parts, of course, which means identifying the problem as a couple and agreeing to work on it. And it could be harder than you expect. But you could both come through it with a wider perspective of the world and of the spiritual possibilities open to you. But as already stated, this takes hard work; if you're just casually involved, it probably isn't worth it.