Any clustering similarity scheme for biometric data would yield similarity categories that we may or may not name "races" though.
We could probably do the same with text analysis, where the emergent distinct flavours would create categories. A previous HN story that did specifically this (https://news.ycombinator.com/item?id=27568709) could have just as easily been called "tribes."
The bigger question is whether the categories provide heuristics with valuable predictive illumination. "Valuable," being the key term to solve for.
Ethnicity information in medicine may be a fast heuristic for testing for things like melanoma and diabetes, but even that this fast sorting rule might provide a time/steps shortcut or intuitive leap to test for a diagnosis is likely really more an artifact of the cost of testing and examination than the result of a physical/biological determinant.
I'd conjecture that a world with tricorders where the cost of scanning for disease is equal and controlled, would likely yield results that were less-ethnically correlated - and then edge cases that were exclusively ethnically correlated, e.g. over a very polarized distribution. There's also the question of whether the tricorder measures complete things, and who decides.
This is to say, there are differences and combinations that may aggregate into categories, but the meaning of the differences is dynamic, subjective, and a function of what level of abstraction you are looking at them from. E.g. at the level of a statement like "most foo people are bar," you've already cancelled out most of the information about your sample, so the coherence of something that low-information is going to be limted as well.
In this sense, the "social construct," description is a response to these noisy dynamics, and it's consistent to a point. In this view, race is only ever a determinant when we let it be, as the result of chosen and learned interpretations of these cognitive grouping dynamics. When the cost of errors is low, we can afford to unlearn these abstractions. Modernity and civilization implies the cost is low.
Taking that further, when the real cost of errors is high enough, you get a reinfocement effect on the bias where the surviving population is made up mainly of people who exercised that fast heuristic (hence long-lived homogenous populations), because the tolerant ones evoltionarily select out as a result of that high error cost.
I could even extend this further to define racists today as people who percieve a high cost to being wrong in their generalizations, which correlates well with being poor, but also, very rich, just less so in the middle between. Anti-racism becomes a kind of signal that shows you can afford to be wrong, and oddly, racism in this model is intended to signal you have a lot to lose. If you want to reduce racism, solve for the security issues for people who percieve a high cost to being wrong about openness. If you want more racism, just antagonize people who percieve that they have a lot to lose. I'd wonder how well that generalizes.