Hmm... well, I think Johnny is a redhead, so I'd say he accounts as genetic diversity as well. Of course, his hair could be dyed - one would need to check his kid-sprite.
either they've been there longer than the majority of the rest of the inhabitants (and are therefore the last remnant of an even older cultural group)
I remember playing with this possibility in my head many times. It usually translated in Cloud being more closely related to the cetras and such, which I'd confirm by looking back to those pools in the Cetra city which he could hear from but not understand. Of course, I don't really have any compelling argument in favor of this - I mostly like this idea because I'm a Cloud fangirl, and like the idea of him being special. There might be better arrangements to this theory - I think being a Shinra family offshoot is a good one.
or they're recent immigrants in the past couple of generations
That is a little more dramatically compelling then the other possibility, as it makes them a much clearer target than "offshoot from the manor from however many generations ago". Principally if they had no clear idea where the new family was from and what drove them to the boondocks of nowhere. Prime ground for gossip and bad rumors.
Oooooor you could mix these. "One of his parents was a Strife, the other a stranger! Keep away from that kid, he might have rabies".
Cloud says in the Kalm flashback that his father died when he was small - one could question that information, considering his state at the time, but I guess it could be taken at face value since it doesn't really add anything to the image of himself he was trying to project at the time. But if his mother was widowed, and theirs a patriarchal society, maybe she was expected to remarry - and maybe a lot of guys were hopping to be the groom (Cloud is pretty enough to give a very favorable testimony of his mother's looks) and hated her for being constantly snubbed. And if she had a child without being married... well.
I get the impression from Cloud that, before Tifa's accident, he was one of those lonely, bully-target kids, who'd look at the other kids having fun with the eyes of a starved puppy. After he was blamed for her fall, though, he started to fight back, both to get attention and out of anger. (I mean, the kids knew he wasn't the one who took Tifa to the mountains, but let him be blamed!) And then, of course, the people who had bad expectations of him felt vindicated in their attitude.
I think Cloud didn't really hide from everyone in the village, only from Tifa. If you talk to Mr. Lockheart in the Kalm flashback, he says "stay away from my daughter". I think it's more likely he'd say such a thing to a low-level grunt he recognized than to a first-class SOLDIER.