If "heap" is a social construct, so is all language, basically, and then everything is a social construct. Sigh.

It is true that all language is socially constructed, but I was trying to draw attention to how "race" is especially subjective. Many linguistic terms are much more precise. A "species" for example refers to related individuals who reproduce among themselves, producing viable offspring. There is still some room for ambiguity, but it is less than what you get with "race". Besides, what's wrong with the idea that all language is socially constructed? It is possible to believe that without falling prey to the fallacy of grey.

Then post-modernists go on to say that if someone in a different culture thinks that the sun is light glinting off the horns of the Sky Ox, that’s just as real as our own culture’s theory that the sun is a mass of incandescent gas a great big nuclear furnace.

I would personally prefer to use the term "better informed" rather than "more real". Hypothetically, if both theories turned out to be completely false, and supposing we learned of that but still had no idea what the actual truth was, it wouldn't be certain which of them is more "real", but it would be relatively clearer which one had stronger evidence supporting it at the time. To give a different example, if we knew that one of the two theories is 100% true but aren't told which one it is, it would be reasonable for us to think it is far more likely to be the theory based on scientific evidence (i.e. the theory that actually aligns with the scientific definition of a theory as being a coherent group of tested general propositions, commonly regarded as correct, that can be used as principles of explanation and prediction for a class of phenomena:).