I was waiting to see, because my nostalgia probably blinds me, but I know it’s 80’s Star Trek. If I had to guess in the misogyny, it would probably be that the outfits for women are completely different than the standard issue uniform everyone else wears. In the first episode they had one guy wearing a Skant, then you basically only see them on women a couple times, then the women lose their brains because they gained cleavage, and lose cleavage to gain brains.
I really don’t have a guess on racism though. As far as I knew, Star Trek was always ahead of the curve on the round of race. William Shatner for all his problems intentionally botched every alternate take of the scene where he kissed Uhara to force them to include the first televised interracial kiss. They even had one episode in OG Star Trek where a race of half back half white people were fighting with the half white half black folks pointing out the absurdity.