During one of our days out, we discussed at length the possibility of a relationship, whether she was interested and whether I was really interested (confessing romantic feelings for her set that discussion in motion days prior), and whether a relationship would work out given our incompatibilities. For instance, she's a practising, believing Muslim, while I'm a generally anti-religious atheist. She believes it is necessary to raise her future children as Muslims, while I'm strongly opposed to choosing any given religion for my future children rather than merely educating them about religions, philosophies, and logic and letting them choose when they're old enough to.
She said she wanted us to remain friends and that she would be there if I ever needed her but that she wasn't interested in a romance with me. Furthermore, after discussing the potential romance, we basically concluded that the incompatibilities--especially in our worldviews and values--were far too significant to allow for harmony or stability in a long-term relationship.
So the romantic interest wasn't mutual, but we did and still do want to remain friends. That is very much mutual, and neither of us has shown any less respect or affection toward the other after that discussion where we pretty much ruled out a romantic relationship.
What do you have in common?
(For us, a shared religious view was incredibly important. We agreed on so many things because of it, like having kids, what jobs to work at, how to raise kids, how much effort to put into stuff, lifestyle, etc.) We were open about a lot of stuff, so when the romance finally happened, it was just easier (from what I've read anyway, no first-hand experience) because we could communicate. But if we'd have been like you guys with really opposing views, there's no way we'd have ever gotten married. Sounds like that would be the totally wrong decision. But then I couldn't be close friends with anyone who was that different religiously either. I don't enjoy arguments.