Character: While I believe the character dimension as a whole is something that people universally care about, there is definitely some dispute among religions as to what actually constitutes fairness and respect.
Satanists, for example, place more emphasis on the self, and so you may find that to be simply, flat-out unfair. Or perhaps you believe that the Abrahamic religions (Islam, Christianity, and Judaism, etc.) place women in an unfair, disrespectful position relative to men. In which case, it’s important to see just how much your partner adheres to a particular religion and which particular sect they’re into. You may find that your partner’s mosque has a similarly liberal vibe as your parish.
Most people’s characters, though, are independent of their religion. In the movie Namesake, for example, the newlywed Indians, Ashoke and Ashima move from Calcutta to Boston and immediately fight over a misunderstanding of gender roles. As a result, Ashima locks herself in the closet. Ashoke is initially upset, but because he is compassionate (the caring factor of character) and flexible (the fairness factor), he sings a sweet song through the door, and assures Ashima that things won’t be like how they’re done in India. She eventually emerges and they have one of the sweetest embraces I’ve seen on film.
Chemistry: One of the reasons people historically married within their religion is so that there would be less disputes about child-rearing or gender roles later on. Now that we have a much more extended pre-marital dating period than in the past, you don’t need to use religion as the same kind of filter.
If your partner has weird attitudes toward child-rearing, it’ll eventually affect your chemistry with that person. When you’re sitting outside of a restaurant, and you see children playing in the sandbox, your partner’s off-hand comments about parenting will either piss you off or accord with your point-of-view. So you should wait till those moments actually happen, rather than assuming that you and your partner will have disagreements because of religion.
In other words, let your chemical sense with your partner do the filtering for you, not the specific religion.