right now Race has some impact on how you're seen in different cities... (Deep elves hated everywhere, I think ogre's are KoS in Keebler treehouse unless they kill a few orcs first, goblins are disdain until killing just a couple there), but I don't think religious based faction has been implemented just yet.
It's also still a little goofy unless there's a lore reason why my agnostic DE paladin is KoS to most factions in NH but amiable to steel talons after one ashira kill populated the associated factions.
I'd say this is all still a work in progress and expect it to be more fleshed out sooner than later.
The only starting city I've not checked faction for on a deep gnome is the non-city guards in AV. (agnostic Deep elves can start in either AV or UD and are not KoS in either - barring the city guards that currently exist to keep everyone out till the city is finished/citizenship quest stuff)