Are the gods aloof and mysterious, do they intervene frequently in the world's affairs or are they narcissistic beings who love to torture their creations just for the fun of it? Maybe the don't even exist?
IMO they have to be aloof. I don't want a lawful good god of magic or anything like that. Making them aloof means that personalities and politics can play a role. If the god's rule is absolute, then how can you bribe a corrupt cleric? How is a crisis of faith possible?
Unlike real medieval western Europe, most D&D campaigns are polytheistic, so I've had to steal ideas from Ancient Rome, China, and Japan (the first having a large pantheon and the other two having semi-competing religions and philosophies). Japan had religious conflict, cooperation, non-violent competition, and syncretism, plus many of the religions were distributed in a way the Catholic church was not, so it's all there.
Marriages and coronations are religious affairs, and smaller religions sponsor guilds and the like. (That blacksmith guild could literally pay homage to the god of craftsmen. So now you know why there might be two blacksmith guilds... they worship different gods!)
Marriages could be a really big deal. What if the king (who worships Paladine) marries a queen (who worships Takhisis) for political reasons? Who is raising the kid? If the heir ends up worshipping Takhisis, can they even get crowned? Probably not, unless they do away with the local clergy of Paladine. (This is an obviously over-the-top ridiculous example. No worshipper of Paladine would marry a worshipper of Takhisis. And even if that somehow happened, the two priesthoods couldn't cooperate on a wedding.)