Where is the "distinction"?
If you're talking about dog breeds, you can identify the specific characteristics -- this is a poodle because ... Tell me again what makes an Englishman "English" or "white"?
I think we're getting into the same old problem of claiming that because there are no sharp divisions, then there must be no divisions at all.
A poodle is a poodle because... there are certain visible characteristics which it has (and perhaps invisible ones as well, such as a herding or hunting instinct in some breeds), which it passes reliably to its offspring if bred with another poodle.
A white person is a white person because... there are certain visible characteristics which he or she has (and perhaps invisible ones as well, but we won't go there), which he or she passes reliably to his or her offspring if bred with another similar person.
I see no difference. I could list the characteristic points for human beings the same as I could for poodles. I could also point to examples of "almost poodles" and "poodle crosses" and "sorta looks vaguely like a poodle but probably wouldn't breed true," just as I could point to "black people" and "mixed-race people" and "sorta looks black but told me he had one Asian parent and one American Indian parent."
But am I really the only person in the world who can tell the difference between people who look like the queen of England and people who look like the Emir of Kano, and also predict that if they have ancestors who look like them, and marry someone who looks like them, they'll also have children who look like them? That's all race means to me. There's no value judgment, neither about what appearance is best nor about whether it's better for a kid to have parents that resemble each other or not.
Of course, there aren't any "breed registries" for people, so it all happens very sloppily and naturally in people, rather than planned breeding to meet a registry standard (thank god). But one can still see similar trends. And if one thinks that dog breeds are nice and neat, one only needs to look at the fights that occur and the constant changes among breeders and breed standards.
So distinctions in humans aren't really "useful"--and honestly, they're not all that "useful" in dogs either, as far as appearance goes, except that we hold dog shows and declare that they are.
But I just can't figure out how to deny what my eyes and common sense tell me, whether it's useful or not.