Exactly ... The term "race" has no definitive meaning with regard to human biological lineage. It's a social construct, and its definition, criteria, categories, and specifications vary with the societies and cultures within which such racial distinctions have developed.
It was recognized as having more to do with socio-cultural affiliations than personal bodyhood / lineage back in ancient times, when (e.g.) the Greeks and Romans considered physical features to vary with respect to environmental factors rather than anything to do with inheritance of permanent form. Back then allusions to "race" were approximately identical to what we now call "ethnicity" (which is defined in purely socio-cultural terms).
The more recent framing of "race" as categories of biological lineages is a much later development, having arisen in Europe circa the 16th through 18th centuries in conjunction with both emergent naturalists' penchant for taxonomic classifications and explorations that had revealed human diversity worldwide. Allegedly 'scientific' and pseudo-scientific racial classification schemes added to the set of classifications available.
Goldberg's error was projecting the merely skin-deep criteria defining her native country's constructs about race (prominent in her life as a black woman of her generation) onto a past European scene within which "races" were identified using (e.g.) more detailed and specialized criteria than skin color alone (as was the case in her own cultural / historical milieu). Her even bigger error was trying to express a single point framed with sloppy regard to two mismatched classification schemes (and insufficient acknowledgement of the differences between them).
It is infrequently that I disagree with EnolaGaia, and even less frequently that I will post my disagreement. But this is one:
People all belong to the same specie: a proof of this is that we can interbreed resulting in fertile offspring. That visibly, genetically, different varieties of humanity exist is also true. These varieties can be labelled with different labels or terms. Race is one term; in the US, this applies to the broad divisions of looking like most of one’s ancestry originated in Europe, Asia, Africa, or the Americas. More problematic in terms of race are the Pacific Islanders, Aboriginal Australians, Bantu, and other, smaller groups. In the US, race is different than ethnic group, which is a smaller subdivision within a race. So, ethnic French and ethnic Russians can be both European racially, but different ethnicities.
These visible differences are heritable via genetics. There are some invisible differences as well, such as the genes which transmit varieties of sickle cell anemia. Yes, some European people coming from the Mediterranean can have this as well, but to date it is an overwhelming African genetic disease. I think that the visible differences themselves evolve over time: for example, dark skinned pre-Beaker people in Great Britain.
But for the current moment, these differences exist and are at least loosely associated with continent of origin. When examined in detail and noting the exceptions, this race and ethnic group categorization breaks down, like many categories dealing with biology. (I love cacti and how the cacti families and species are always being re-organized. It never flipping ends as weird exceptions are found and shoe-horned in somewhere. Cacti have high genetic variability, as do humans.)
Whatever the term used to denote these different groups will, it seems, inevitably be used to assign a social, political or economic status. This is an unfortunate part of human nature.
To deny that these difference exist on a physical basis because of disagreement of the social status assignment is not good science. I suspect that this well-intentioned effort will have unintended consequences.
The problem is not with different types of people, nor the categorization schemes (races, breeds, ethnic groups, etc.), but with the use of these terms for in-group and out-group distinctions. Long after we are all dead, I hope that these differences will disappear, both genetically and socially. And the sooner the better!
As to the point that we are all one race: to argue by analogy (God forgive me), if we were discussing dogs, and claimed that all dogs were one race, then the differences between great danes and miniature poodles would have no genetic basis.
I am a mongrel genetically, with input from a wide variety of ancestors. But I look white enough to be a target for some nonwhites to act out on me. I think my claiming “But we are the same race!” will not deter them, as they identify me, based on physical aspects, as an out-group member to them.
It is the social construct, not the physical reality, which is the problem.