I care less about what denomination they consider themselves apart of and more about how they interpret scripture. For example I am a Calvinist, do I care if she was a Presbyterian or Dutch Reformed, say? Not really, because doctrinally speaking they're basically the same. Now if she were a catholic, the differences there go well beyond "minor differences", we're talking about major theological differences. Could we get along? Of course. Could we have a stable marriage? Probably. However, what am I supposed to teach our children if it ever comes to that? If both parents are teaching a different doctrine, that is not a unified household.
I will say that in the past my answer would have been I didn't care, so long as they were a Christian, but now, I mean, it's more than just "I'm presbyterian" or "I'm catholic"...etc. we're talking about major theological differences, the biggest of which I can think of off the top of my head is each respective group's teachings on salvation. You may choose not to think about topics like that or look into it or think it matters, but when you are raising children and you are instructing them on the way they should go, which way do you tell them? How do you instruct them? Which way is right? Because if the father is saying one thing and the mother is saying another, that's just not a unified household, and I don't think that will end well, or at the very least will not be as effective as it could be if both parents were on the same page.
Anyway I'll leave it there.