I'm deeply religious and lean more towards the Evangelical Conservative side.
I'm not picky about DATING girls from different religions. But casually "going out" a few times is different from a serious relationship. Also, if I'm in a serious relationship, I still don't have a problem if she's of a different religion as long as she understands that my beliefs are very important to me. I don't think it's wrong to share my beliefs with someone I'm seriously involved with, but I'm not going to ram that down someone's throat.
Of course, we're talking about dating and not marriage, which is an ENTIRELY different story. When my wife (who came from a long line of Methodists) and I started discussing the whole matter of religion, how we plan to raise our children in a religious community, etc., and knowing how how different our own backgrounds were and how important my beliefs are to me, we never reached a good, workable solution. I simply told her to pray about it and I'd do the same. Eventually she saw something in my church she felt was missing from her own, so the point became moot. She "converted" (not sure if that's the right word, we were both Christians to begin with) and that was that.
When it comes to dating and religion, I generally believe that "steel sharpens steel." I have a tendency to be a domineering guy when it comes to my faith. Even though I don't ram it down someone's throat and try to be tolerant, anyone who's ever been with me knows it's impossible to ignore long-term. I once dated a Unitarian/Universalist, which to me is a funny anti-religion under the guise of proclaiming all religions equal. For her, being dragged to church every Sunday (she could have said no and I'd have been fine with that) wasn't a problem because of her tolerant views of religion as a whole. This was something she was diligent about as long as we were together, but after breaking up she quickly fell away from it. I think it's BETTER to try to stick with someone you share a common faith with because you have the chance to hold each other to those beliefs. I actually have a part-time job at my church, and they rely on me so much that I can't just casually decide not to go. My wife finds it annoying sometimes because that makes it difficult for her NOT to go as well, especially since we have children (I'd just take them anyway, and then she'd be bored at home with nothing to do!). Her faith is much more "child-like" than mine, so even when I'm having some personal crisis, I lean on her to keep ME in line. So between the two of us, it's easy to hold onto our beliefs and keep our marriage and family strong because of how strongly each of us feels about it.