As long as:
1. They were not an atheist: I would not one to be married to someone who, ultimately, thinks I'm talking ********; I'd find it passively antagonising, like I'm being judged negatively if the conversation crops up, or like I'd have to hide it, even though some of it would be in my head. This is probably my most controversial position because of hurt feelings.
2. They were not like your typical misotheist, LHP Satanist (theistic or atheistic) and similar groups like that: I don't mind the LHP, but I find misotheists to be angsty, and I often find some LHPers to be a little... well... too fruity for my taste; we'd rub each other up the wrong way. Some LHPers, I'd have no problem with, but others... meh.
3. They were not a fundamentalist: I do not want someone who is completely crazy about things and lets it run their life to extreme measures where it interferes with the relationship.
4. They weren't away with the fairies: I want someone who is a little bit sane, so I don't feel like they're going to stab me in my sleep.
5. They were not hostile to my own beliefs: self explanatory.
6. They respected my right to believe and did not force their beliefs on me.
7. They weren't a creationist: no, just no.
8. Anti-theists: I wouldn't touch them with a pole. Even if I had no faith. I find them intolerable and cancerous.
9. Someone who believes I'm going to hell for believing differently to them: for a similar reason to 1. I wouldn't want to be married to someone who thinks I'm going to suffer for all eternity. I feel it would be frustrating for a relationship.
I'm already married to someone with whom I don't share a faith with, though.