In an attempt to jump start the conversation, let us expand the context of incompatibility somewhat. What if your marriage partner is actively engaged in separate activities that go against some of your core values?
For example. You are a devoted wife and your husband is equally devoted to you. He fusses over you, buys you flowers, helps you with the housework and the kids, works hard to provide you with a comfortable life. However, he likes to look at pornography on the internet when he knows you're not looking. He likes looking at naked women, but also couples engaged in sexual activity. Sometimes he even likes to look at naked men, too. Take it up a notch. When you're away doing the things you like to do, he likes to dress up in women's clothing. When you're away for a few days and he really wants to be naughty he goes to the supermarket and purchases baby zucchini or some other slim vegetable with which he indulges in what might clinically be described as sexually deviant activity. He does nothing to break the law, nothing that directly does harm to you, indeed nothing that does harm to anyone. In effect, he honours the Golden Rule, but his private activities are to you repugnant, as they would be to most people. And just to forstall snide conclusions, no, I am not talking about myself, although I do have a good friend whose husband, tired of his secret life and seeking his wife's understanding and participation, confessed to her after more than 25 years of marriage that he was engaged in exactly the things I describe above.
Here's another example, more germane to the context of this board and this particular conversation. You are a devoted and loving husband and your wife is equally devoted and loving toward you. She bends over backwards to please you, although there are limits to how she will please you, imposed by her values. More precisely, imposed by the values of the Society to which she belongs and to which she is entirely devoted. Although she does her best to minimise your second-hand exposure to her Society, on her own time she actively engages in promoting doctrines that offend your values, on the basis that they do demonstrable harm to others. Some have died as a consequence of blind adherence to those doctrines, including children, although you don't personally know any of them. More personally disturbing to your closely held values, she is also shunning members of her family - refuses to talk to them, even to be in the same room with them. She seems to have two different personalities. One that is devoted to you and your relationship together, another devoted to her relationship with her Society. The Society is, in effect, the third party in your marriage and in your marriage bed, a third party that tells her that you are spiritually inferior to her and everyone else who belongs to her Society. You detest the Society so you, in effect, offend her values, too, but she loves you deeply regardless, as you do her.
I suppose one could argue the virtue of compromise, but practically speaking there are always limits to compromise. In the first example, my good friend left her husband, and who can blame her? In the second example, my own as it turns out, love has prevailed but the relationship has suffered. Neither one of us is completely happy but, I suppose, happy enough that we stay together.