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Yes, denying that there are differences of physiology between various members of some group of organisms would be woefully ignorant. However, denial of physical attributes and their genetic ontology is not at all the point of understanding race as a social construct.
The point of understanding race as a social construct (and incidentally, of understanding disability as a social construct) is to
1) accept that there are differences between us
2) accept that those differences, because they are marked and visible, have provided for us a means of categorising people
3) deny that those categorizations should come with the traditionally-upheld value judgements.
For instance, black people are not innately less valuable than white people. However, evidence shows us that black people ARE valued less. (The Black Lives Matter movement tries to show us that police have a tendency to shoot argumentative black people, and a tendency to give white people a chance to argue.)
This value judgement is what has been constructed.
The construction has its roots in imperialism of African labor. Imagine someone who is a totally different skin color shows up in your town and puts you in handcuffs, puts you in a boat with hundreds of others and makes you row in order to avoid getting whipped and earn some food. Then the boat lands, the people with the whips trade you for money, and the landowner that bought you takes you to his farm and makes you do work....provides you with no education that would help you even begin to cope in this new, strange society where the landowner has a whip and you don't. Generations--and that is a very very important word--generations of black people were brought to the US and placed under these conditions. How can they possibly get a leg up? For this reason, black contributions to US culture have been re-appropriated (into jazz for instance) but not valued. The understanding that deeply permeates US culture--whether we are willing to admit it or not--is that black IS innately less valuable than white, unless black has been snatched up and incorporated into white culture, whose roots are largely traced to Western Europe.
The value judgements are embedded in art, the media, literature, the educational system.
The point of calling race a social construction is to provide a starting point for beginning to dismantle the value judgements and begin seeing people as individuals, not simply part of their category.