I think the big difference between the Clan and the Doviello is the reasons they would fight other civs.
The Clan seems to be more based off of the worship of Bhall. The Clan loves to fight, but NOT without reason. If you insult them, you better gear up for war. They don't fight purely for the sake of fighting. So, they'd prolly view a religious war a good reason to fight. The whole 'Our God is the true god' syndrome. They need essentially a passionate excuse to fight. They won't jus fight cuz they're bored.
But the Doviello are really the kinda people, who as a group, don't care a ton bout religion. They really don't give two cents if their neighbor is a follower of OO or AV, unless of course they can use religion to start a fight. It isn't that they really believe one religion is better than the other. They jus see religion as another way to brawl, war, and kill. Essentially, they fight cuz they need entertainment. So, a war to them is jus a bigger form of entertainment. It's like when me and my friends go out to drink. We don't have a reason to; we jus wanna get drunk. (Spare me the moral BS, ok?)
That's how I see it I guess.