My 2 cents. Bein older, and a staunch believer in equality, I refuse to do any of these things for woman. I was around in the feminist movement in the 70s, and have done my thing for equality all my life. Sexism is the discrimination I have fought hardest against. After the womens movement, and the subsequent shift towards equality within the sexes, I then thought it hypocritical to open doors or pull out chairs for women, or other such things.
It needs to be realised these things were first put in place by men, under the umbrellar of doing things for "the weaker sex". Women, were soft, fragile, weak, and needed caring and looking after. It was very much entwined with the sexist view of women being "less than".
So no, I point blank refuse to do anything for a woman, simply because she is one. However, I will open doors, pull out chairs etc, simply because it's a nice thing to do. I am also happy for a woman to do these things for me because of the same reason, its a nice thing to do.
Because I'm so much older, I often have old school women waiting for these things at times. ha ha, bad mistake, they wait for a fair while lol, and it don't happen. That's it for me, expect it, or wait for it, it won't happen. But I will do it of my own violition because its simply a nice gesture.
Hence the strong rules on our game server regarding sexism btw lol.
Cheers