That is rubbish. A straw man. I've spent more than a decade within the so-called Overton bubble at a university, and this is decidedly not the consensus as I experienced it.
All biology is known to yield population variation. That is obviously true by necessity. However, there are both ontogenetic and phylogenetic influences on outcomes. The progressive/egalitarian view is that the cultural dynamics that result from small population differences (that are in any case too high variance to be reliable for making individual discriminations) should not inhibit phylogeny. Put another way, an individual's self-expression should not be limited by the fact of their membership in a particular category.
Further, while there may well be, in lab settings, reliable significant population level differences, these differences at an individual level may entirely be swamped by cultural influences, rendering them insignificant.
Lastly, the sources of the population differences may, in some instances, be factors that are entirely culturally malleable. Males as a population may have a slight predisposition not to understanding mechanisms better, but instead to finding them interesting, which over the course of development leads to greater competence. This predisposition may be easily changed at a young age by an encouraging mentor or compelling Hollywood film. Similarly, someone may be predisposed to kidney failure not because of bad kidney cells, but because they don't have as strong a compulsion to drink water (a deficit trivially remedied).