EDIT: Some replies suggest that I may have been unclear. The social grouping into race is obviously not random, but based on perception of visible morphological attributes. However the categorization that results is probably not the same categorization that you would get if you looked at the whole genotype and tried grouping humans together based on genetics. One basic fact of human genetics should guide you here: there is more genetic variability within any socially constructed "race" than between "racial" groups. So claims that common racial categories correspond to big differences in genotypes don't make sense. Whether there are races at all in humans is something that biologists disagree about, with most at the moment saying "no". Whether race is useful to medical diagnosis is also contentious. The human species is unusually genetically uniform. Most animals that all look about the same to us, like chimpanzees, have (in that case) about three times our genetic diversity.
If you look at genetic population groupings, the gap between populations that the layman would identify as "black" and "white" is as wide as the Sahara Desert. Literally so, if you put these population groupings on a map.
It's true that, if you look at New World, non-indigenous populations, things get more complicated. But genetic populations still correlate very highly with geography and ethnicity. The layman'a notion of "blackness" or "whiteness" may be flawed, but it's not completely incoherent.
On forms, I never answer any question about my supposed ethnicity. How would I even really know? And why would I care? If there is some word with a capital letter that is the name of my supposed tribe, and all my heritage is attached to that, I hereby throw it in the garbage. It isn't worth it, if it's a wall between me and other humans. The special dance of my ancestors, the special holiday tradition, blah blah blah, on and on, whatever, I reject it, and choose to be a generic mutt in the one real tribe there is, called the human race. To me, that is progress.
This is not overly surprising because "race" is a social construction, not a biological category, and individuals of ambiguous racial admixture are not uncommon today. Take for example Congressman G.K. Butterfield, who is constantly subject to questions about his membership in the Congressional Black Caucus among other topics, despite having two parents of visible African ancestry. http://en.wikipedia.org/wiki/G._K._Butterfield
The real point is that racial categories are silly. Humans are remarkably genetically similar across the globe. There is greater genetic variation in two chimpanzees from the same troupe than there is between humans from the tip of Patagonia and the Khoisan in Africa.
Perhaps it's like not necessarily having convictions about others, but just allowing others and ourselves to change our opinions.
Occasionally, people ask them why they have so many black friends or tell racist jokes in front of them. Other times, people who believe that they share a common heritage will speak to them in languages and become angry when they don't understand.
Human beings are all to apt to judge a person's ethnicity by their appearance, but in many instances one's appearance is not an accurate gauge of their ethnic heritage.