Truth limits freedom. Psychopaths can't thrive in a society where trying to be objective is the norm.
I'm not saying all people promoting this "social construct" idea are psychopaths. Most are just indulging themselves in the pleasure they get from caring (for victims, real and imagined) and denouncing (their own group). The psychopaths learn what will get other people to do what's best for the psychopaths.
Yes. I think that the whole anti-truth word-salad is designed as a narrative offered as justification of any and all moral transgressions its proponents have committed in the past or plan to commit in the future. If nothing is true, then everything goes so leave me alone to do as I please. They only express sympathy with 'oppressed' groups so they will not be condemned for their own tresspasses themselves later. But because it is presented as a defense of the oppressed, many people fall for it and think it's a good thing.