It's not that they're undead. It's not that they smell bad, or that they eat people, or that they roam the night in a shambling mockery of their prior lives.
No, the problem is that zombies eat brains. This means that they'd be more inclined to eat people with bigger brains.
I submit that if zombies wanted to eat people with small brains, that they would actually be a valuable socio-economic force in America. Zombies, rather than being seen as undead predators, would come to be seen as an important part of the cycle of life, and a priceless contribution to the quality of the human gene pool.