It would make sense for colonies to have sympathies in line with the parent realm, but I think all new realms get new neutral sympathies at the moment.
Though, it would be bad ass if the religion were to influence it. I would assume you would need yo implement state religions for that, though. As cool as that sounds to me though, I THINK that's an already proposed and rejected idea.
I agree it would be cool, but I cannot imagine how hellish it would be to code.
As for how the current system works, I have no idea. It neither seems to default the same in every region nor use the parent realm's. Random, maybe?