Racial segregationists in the Americas literally had to write laws delineating races based on factors external to that individual (e.g. their parentage). That is: even people who believed in a racial hierarchy also believed it was not possible to objectively identify a person's race without knowing e.g. the races of that person's parents.
Race has never been considered a generally observable fact about a person.
If an arbitrarily large grouping of genotype combinations is necessary to categorize people, perhaps that categorization scheme is not useful? I would imagine that the number of "races" generated via the mechanism you posit would measure in the hundreds or thousands, rendering it unrelated in practice to the word "race" as it is used.
Could you give a reference to someone who actually says this?
Agreed, and upvotes too! It seems like I've struck upon something people have been interested in talking about.
> The other replies here are mostly good, but I'd also like to note that "race is a social construct" refers to how "races" aren't really objective categories (What defines if somebody is "white"?) and more of a subjective thing, particularly at the margins. We can build classifiers that can match most people's (in our current cultural context) perceptions most of the time, but that doesn't make it a rigid natural phenomenon.
I certainly believe this to be the case, but when I hear "race is a social construct" it's almost always in the context of denying biological differences between the races in the same way that some extreme (though mainstream and influential) people take "gender is a social construct" to mean that literally all differences between the sexes are socially constructed including height, weight, strength, etc (otherwise known as "blank slatism").
That said, unlike biological sex, there are fewer valid social implications that we can draw from race (e.g., there are a bunch of social implications which fall out from women's unique ability to bear children, but no analogues which fall out from race) and we have drawn many false implications from race which have been tremendously harmful to individuals of different races, so if we have to reduce everything to a slogan or a binary (as our simplistic society increasingly demands), then "race is a social construct" isn't a bad one.