The standard vampire has a lot of Christian elements. This doesn't mean you couldn't do a Jewish vampire story (maybe it's not crosses, as such, maybe it's faith--or maybe as in The Keep crosses work because they're related to something else), but you'd have to do some reconfiguring.

I've seen some speculation on what obligations an Orthodox Jewish vampire would be under, but no conclusions. Jews aren't permitted to drink/eat blood, even animal blood, but you're allowed to break that sort of rule to save a life. Does what a vampire count as alive?