Those people should probably read more. While a social construct does not have an absolute origin, that something is a social construct has never implied that it’s “fake.”
Especially at the level of the individual, where the gender “construct” becomes a monolith and internal and external perceptions belong to one person, it contains the entire definition for that individual at a point in time. So for the individual at a point in time, the construct is not only real, it’s literally all there is.