Well, I think you need to define what you're actually asking. What someone actually believes or not does make a fundamental conflict. A religion is a club of people who may or may not actually believe the same thing. For those who are part of a religion without actual faith, yes, it probably wouldn't be a problem. If you truly believe in your religion (or lack therof), it would probably prove difficult.
At least for a pair with a Christian believer in it:
If you truly believe in Christ and his full teachings, you're going to want your significant other to believe, because you would want everyone to believe, because you want everyone to have a personal relationship with Christ. Especially your loved one, as the idea behind Christian marriage (not saying it is the only definition), which would be your ultimate goal in the relationship (if you truly believed), would be the union of two souls in Christ, following in service of the Lord together. Also, you'd love to see them in paradaise, equally, you'd hate to see them in hell. If you believe just "being a good person" gets you into Christian heaven, you don't believe Christ, because he said himself the only way is through him.
If you truly don't believe in anything, you tend to be the sort who thinks that those who do believe in something are idiots. Of course I'm generalizing, but if you have a truly Christian significant other, they're probably going to annoy you.
I can't speak for other faiths.