I would add that religious institutions were also more likely to have common ground because for many of them their realm threats were the military infrastructure. Yes, foreign religions were wrong and evil, but they were also unlikely to challange the idea of theocratic rule. Powerful civil and military leaders did pretty much constantly.
I may think your religion is loonytoons, but there are solid political-economy reasons to at least pretend to have contact. After all, we may disagree on the sky being blue, but all religions tend to believe in the importance of religion to the state.
