Not only does one or both parties being religious or not matter, it also depends on what religion is to you. Actually, basically it depends on what relationship is to you. While I appreciate that intellectual stimulation can be a part of it, I don't see relationships as a matter of thought process alone, or any process at all. All of that may be there, but the bottom line is what are you about, what is your life about, (or what life is to you) and how does that fit in with the other person - or whether it does fit. I guess I would say the processes is just how that plays out.
It's a challenge to find someone who thinks similarly as you or not, but it's even harder to find someone who doesn't live life based on thoughts and beliefs. Actually, that's what we all want isn't it? Sure you might find someone who believes a certain way, or is smart and interesting, but these factors alone do not automatically make someone you'd want to be in a relationship with. Isn't it true that sometimes you can look at someone who is otherwise very attractive in different ways, but there is just something missing?
And not to be negative, but frankly even when you like everything about each other the relationship doesn't necessarily always work out anyway. Whether it's geographical distance, career or whatever, life situation sometimes just does not match up like the people do. Sure we can work on that, and that part of it is a process, but when life isn't just about that perfect girl or guy, you just don't drop everything else and focus on the relationship exclusively. We may have other relationships in our lives like if you're a parent and so on...
It may seem rather difficult, but I think the key is to not compromise how you want to live, and then the relationship part will be in context of the life you want to have. Of course there's the give and take, but the bottom line is finding out what is really important - then we can let the rest of that go.