When it comes down to it, I don’t think intellect, political or religious ideology or any of the things people seem to find astronomically important really determine compatibility. Some common interests like a passion for music or sports can bring some people together and get the flame started, but in many cases opposites attract and how can you explain that?
What makes two people compatible is their ability to always enjoy and treasure being around each other, trust each other, compromise, and sacrifice for the relationship. You can’t really rationalize why you love another person or write out a list of traits that makes a relationship “work”, and I guess that’s what they call “chemistry”. That’s why dating websites aren’t foolproof. There’s more to compatibility than the concrete.
I think if two people find it worth working through their differences to keep that chemistry going, they’re compatible.