The compatibility issue here is a question of tolerance. And that's a two-way street. An avowed, aggressive antitheist is not going to get along well with even the most milquetoast believer. Nor will a missionary or an apologist get along well with an atheist. For such people, the assertion of that identity is simply too important.

I've had relationships in the past with believers. It was fine, so long as we understood and tolerated this difference. I was fortunate to be married to another atheist and it would be easiest to form my next LTR with an atheist, but I don't view that as an absolute necessity. But is an absolute necessity that she accept my atheism as a part of who I am, and if she happens to be a believer, that she not be threatened by it.

I got out of a relationship where we were both non-believers and am now in a relationship where my partner is a believer. We've been together almost a year now. Although I had a lot more in common with my ex, my partner now and I get along a lot better. My ex and I disagreed or butted heads on a lot of things and there was a lot of underlying tension/anxiety a lot of the time, but with my now partner there is nothing like that. We never argue, we always speak kindly to one another, and there is no drama. It's a much more laid back and calm (normal) relationship, which is a relief. Although our conversations aren't quite as interesting and intense, I appreciate the fact that I can just be myself and relax for a change.