To be fair, I don’t think you should cut family members who are sexist, homophobic, racist, etc. But you can chose to protect others from them by not forcing social situations where they would made others uncomfortable or even hurt them.

Also, sometimes you can influence not by trying to argue, but using other subtle tactics. I mean, with my uncle what worked was treating him as if he was a little children misbehaving (yes, he is older than me, but if he acts like a spoiled brat, that is what he gets). Sometimes you can “twist” their own social rules to force them to act more decent. I mean, fo some people if you tell them they are sexist is a badge of honor, but if you tell them that since they can’t do something and act as if they were “helpless” for not doing that on their own, they might do it just to “show you”.

But don’t feel bad about the people who won’t change. Just one person who gets it is a win. It is not an all or nothing situation. Change is a path. Even with sexist people who remain sexist, it might be a win if they accept some changes like helping a little or just not taking for granted that other person do the domestic chores. Step by step. You should celebrate the small wins, otherwise we’ll became exhausted.