I'd tend to say, if the supernatural someone still thought of the place as home (and their family still lives there), they could get in. This would, imo, immediately rule out DF Black Court vampires - they're sufficiently inhuman that the concept of "home" doesn't work for them. A White Court vampire, on the other hand... though, of course, the WCV could walk through an active threshold with no problem; it would merely limit the amount of supernatural power they could bring to bear.
In general, I'd say the creature needs to be something that is capable of generating a threshold before it could claim free entry on the basis of somewhere being its home. So, probably not Red Court vampires, either. Scions of most types, sure. Dragons (even those with a lower case 'd'), sure. Kitsune (but probably not kumiho), maybe tengu, definitely not fae (Though they get their own exceptions...), and so on and so forth.