The claim about diversity within group vs between groups is true, but only when talking about individual loci. When you look at multiple loci and take into account correlations, then “racially different” populations start to cluster: Check out the diagram here, and look at this. See also the analogy to culture here:
“It should be terribly obvious that almost all variation in people’s cultural traits is within-culture rather than between-culture. Do you play the piano? Speak Chinese? Eat meat? Vote straight Libertarian? Have gay sex? Go to the zoo? Certainly there is more variation among individuals within California in all of these areas than there is between the average Californian and the average New Yorker.”
Does this mean it doesn’t make sense to speak of California and New York culture?
I’m not sure how meaningful your third point is. Regarding your fourth point, the inconsistency between traditional racial categories, I’m not suggesting that ALL racial categories are equally meaningful or good or that we are currently using very good ones. What I’m suggesting is that the everyday racial categories we use are a better clustering of the data than you would get if you randomly assigned people to groups. In this respect, racial categories have a degree of biological reality (i.e., they aren’t freely constructed).
Regarding your other point about the possibility of subdividing categories: If you distinguish a downpour from a drizzle, yet I call both of these rain, is this evidence that weather is not real? Since I can further subdivide US culture into northern US culture and southern US culture, is this evidence that culture is not real? “Black” could be considered a racial category, as could be “African American”. The latter is more precise than the former, yet I would assume that both contain some level of information that would allow me to make certain predictions about genetics better than chance. Categories don’t have to be clear cut or non-overlapping to be meaningful. I’m not arguing that “race” is a good term for commonly used racial categories, and its quite possible that commonly used racial categories don’t qualify as “races” in some strict biological sense. My argument is that our common-use racial taxonomies do cluster the genetic data better than just randomly putting people into groups.
Regarding the fifth point, again I’m not saying that all racial categories invented by humans make sense, just that commonly used categories have some “genetic reality” (i.e., more than assigning people to groups randomly).