Heaps can be said to exist because of vagueness in the definition of what precisely makes something a heap. Race is the same way, which is why it is a social construct. I'm not saying that "heap" and "race" are not useful terms. They do correlate with actual differences, but they are social constructs because they are convenient simplifications to help us describe phenomena.

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

Maybe this will help -- hot off the bit presses:

Post-modernists sometimes say things like “reality is socially constructed”, and there’s an uncontroversially correct meaning there. We don’t experience the world directly, but through the categories and prejudices implicit to our society; for example, I might view a certain shade of bluish-green as blue, and someone raised in a different culture might view it as green. Okay.

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. If you challenge them, they’ll say that you’re denying reality is socially constructed, which means you’re clearly very naive and think you have perfect objectivity and the senses perceive reality directly.

Plus, you might be interested in the wonderfully named Troll's Truisms:

A Troll’s Truism is an ambiguous statement by which an exciting falsehood may trade on a trivial truth. For example, ‘morality is socially constructed’ sounds like a radical assertion of cultural relativism until we are told that by ‘morality’ the speaker means not morality itself but just our beliefs about right and wrong. Of course, these beliefs are, in some sense, socially constructed, if only because our acquisition of many beliefs is mediated by language and beliefs about right and wrong are certainly among those acquired in that way. Hence in this sense of ‘morality’ the statement is true and trivially so.

Heaps can be said to exist because of vagueness in the definition of what precisely makes something a heap. Race is the same way, which is why it is a social construct.

Right conclusion, wrong reason. (The first sentence strikes me as incorrect all by itself. I could still call certain things heaps even if I had a sharp definition of a heap.) Race is a social construct because genetic data underdetermine racial categories.

Expanding: although knowledge of human population structure rules out (or at least makes implausible) many potential racial classifications, many other classifications are compatible with it. Therefore an analyst has lots of latitude to decide which genetic differences between groups constitute races.

(The continuousness/blurriness of human genetic variation is mostly a red herring, though it does sharpen the under-determination issue and make it more obvious.)