Something being a social construct means that when we group people by the trait, the boundaries we use are socially defined. That does not make the underlying trait mutable.
Race, for example, is entirely defined by genetics and interpretation. The former is not mutable, and it doesn't matter that the latter is mutable.
It's like the difference between blue and green. The boundary is a social construct, but the way an object reflects light is an immutable characteristic. No matter what you classify an object as, you're making that decision based on an immutable characteristic.
