I'm well aware of that argument. As user hakfoo noted, the underlying spectrum (if we want to call it that) is biologically real, it is only the human categorization into (more or fewer) groups that is lossy. But this is the case with nearly everything, including color, yet we wouldn't say colors are a social construct and there's no physical difference between red and blue. Especially since those "muddy, unscientific" classifications correspond so well to observed genetic clusters.
It gets very, very hard to classify people into neat little groups when you have a multi-generational mixing pot such as the US.
This statement implicitly accepts race as biologically real. That it can't be fully described with "neat little groups" doesn't make it less so.
Is race passed down the mother's line? The father's? Or does it arbitrarily transform between generations due to some biological facts I'm unaware of?
Scientifically speaking, what are the rules?
Try applying the same logic to any other concept - it is nearly always the case that concepts in language do not perfectly describe the underlying reality. Yet we're not stupid enough to then claim that means the underlying reality is meaningless.
Can they really, though? Most people would identify me as "white," but as a 100% Slavic person from Russia, how much do I actually have in common with "white" people from Italy, or "white" people from Ireland, or "white" people from South Africa, or most "white" Americans? You might have to go back many centuries to find some common ancestry.
Is an olive-skinned person from Greece or southern Italy "white"? Today they are, but they wouldn't have been in the past. It took a while for them to acquire that label: https://www.nytimes.com/interactive/2019/10/12/opinion/colum...
Should a light-skinned person with 1/32 black ancestry be considered black? They certainly would have been in the Jim Crow era, but Susie Guillory Phipps sued over this to change her recorded race to white.
Is "hispanic" a race? In fact, many latinos actually consider themselves white: https://www.npr.org/sections/codeswitch/2014/06/16/321819185...
Et cetera. There are certainly genetic differences between populations, but "race" as it's understood in popular culture (based on superficial phenotypical differences) is a muddy, unscientific classification. I'm not a social scientist, so feel free to look up "race is a social construct" to find more authoritative sources. There is a very high degree of academic consensus on the subject.