I despise the category of "social construction." "Race is a social construct." "Gender is a social construct."
It confusingly conflates these three:
Socially Constituted: Something that only exists because we say it does.
Socially Chunked: Something that exists as a spectrum in the real world that we—with some arbitrariness—chunk into discrete categories.
Socially Charged: Something that exists in the real world that we decide to assign social importance to.
Examples:
Socially Constituted: country borders (They only exist because we believe in them. If we decided there is not border between Canada and the US, there wouldn't be one.)
Socially Chunked: colors (There are real electromagnetic wavelengths in the world that don't depend on our beliefs, but it's our choice to lump cyan with blue.)
Socially Charged: holding hands. (We decide what holding hands means socially but holding hands exists in the world and does not exist on a spectrum that we arbitrarily chunk.)
Socially Charged & Socially Chunked: mental illness (There's real mental variation in the world that exists on a spectrum. We decide how to chunk these and give those chunks social significance.)
I hope these will help you think more clearly about race and gender.