Having had one with both, I can say that the religious differences were way worse than the political differences.
I became a scapegoat for her religious guilt, because “the man is supposed to be the religious head of the household”, so anything she saw as a shortcoming in herself or of the family spiritually was directly attributable to my lack of participation in her eyes.
Moreover, it strongly colored her morals about everything else, including her politics, to the point that some of the political views she maintained per her religion were at odds with her own actual inclinations.