The division is largely because “the left” (in which I include myself) is heavily bound up with supporting the underdog, the oppressed minority, of being tolerant and open-minded. The rhetoric has overwhelmingly been #BeKind so anyone with GC views is necessarily #Unkind and right-wing to boot.
I suspect many Labour politicians feel trapped in identity politics despite their misgivings, and they seem to think there are more #BeKinders amongst the electorate than, er, women (51%).
After 13+ years of Tory government I cannot bear the thought of being stuck with them AGAIN all because of the ridiculous current gender ideology fad/craze/contagion.