Well, I haven't read the book either, but most of the meat of your question is in the presumptions it makes. Let me address them respectfully.
The main thrust of your post is that race is an objective reality but that studying it is politically incorrect. It is true that racial theories will tend to be dismissed as crackpottery. But there's more to it than just the bad aftertaste of Nazi pseudoscience. First, race as a scientific concept is too squishy to become a useful theory; it generates too many intuitively attractive hypotheses that can't be tested empirically; and that invites us to interpret myth as fact.
Case in point: the Germans. My sister married into a family from Germany, and my daughter lived for awhile in Hamburg and made many friends there, and guess what? That's an awful lot of blue eyes and fair hair. The temptation is to think this is the genetic heritage of the "German Race"; that it comes down to them from a small group of fair haired, blue-eyed proto Germans in the far distant past. But there's no *evidence* to support that; it's just a satisfyingly simple myth.
There are nomads in very "Yellow race" looking Central Asian steppe tribes that have blond hair and blue eyes. Aha! Some adventuring proto-German probably spread his wild oats on the Silk Road! But that's the *myth* speaking. The facts are *equally* consistent with the genes flowing the other way, or flowing to both places from a third source, say the Slavs. Even if we presume that the sharing of these features is due to interbreeding, the facts don't support one scenario over the other. Julius Caesar doesn't mention the appearance of Germans in his account of the Gallic Wars in 51 BC; they might have been light-skinned, fair skin and blue eyed as many Germans are today. But they *equally likely* might have been none of those things. A few hundred years would easily suffice for such features to go from rare to very common in such a small population.
But the idea of "race" as we have received it is very definite on the matter. Take the case of one Frederic Austin Ogg, an otherwise intelligent and educated historian writing at the height of the respectability of "racial science":
For my own part, I agree with those who think that the tribes of Germany are free from all trace of intermarriage with foreign nations, and that they appear as a distinct, unmixed race, like none but themselves.
Yes, but *why* did he believe this? What evidence did he have?
Well, we now have genetic information now to address the question of how racially pure of the Germans are. The answer is, "not very". There was plenty of "intermarriage" (or at least inter-boinking) going on between Germans and others, even apparently *Africans*, although not necessarily *directly*. But the genes don't care, they just spread themselves as far and wide as they can. And that's the norm with humanity: populations are too genetically permeable for pure-bred peoples or "races" to exist.
If you go beyond a few superficial features to the whole spectrum of genes, the various three and five race divisions of the human race that were concocted in the 19th and early 20th C all fall apart, and a more complicated picture of extensive interbreeding emerges.
That should be a final nail in the coffin of "race", but science provides one more, a painful rejection for advocates of racial purity and self-love: Most of the genetic diversity in the human race resides within black Africans. So if you were to start with the *genes* and divided humanity into five "great races", what you'd end up with is four somewhat arbitrarily grouped African races and one catch-all race for everyone else in the world (e.g. Germans and Celts would be in the same category as Dravian Indians and Australian Aborignes).
Now any one can see dividing humanity up into "races" this way is useless, but in fact there's actually *more* factual support for this than any of the three race or five race schemes of 19th century "racial science".
And here we have why "race" is such a *scientifically* reviled concept. The appeal of "race" isn't how it fits the facts, it's how it uses very selectively chosen facts to reinforce preconceptions. It's such a seductively powerful confirmer of preconceived belief that no matter how thoroughly the concept of "race" is smashed against the anvil of data, there will always be people trying to piece it back together again. And that makes it a nuisance for anthropologists, the way perpetual motion is for physicists and crackpot *DaVinci Code* theories are to historians.