If I see somebody struggling with packages or something else, I hurry to open the door for them. Or, if I get to a door just before somebody else does, I open it for them and stand back, to demonstrate civility and humility. As in, I got here first, but I'm not going to go through the door first, because I'm not competing with you.
I don't distinguish between men, women, or non-binary people when I do that.
Sometimes I get weird looks from men. That's okay. They can feel weirded out if they want to. Their choice.
On the rare times that a woman has told me she's capable of opening the door for herself, I've simply stepped back further and apologized.
Of course, as a gay man, I don't date women. So none of that comes into play. But I don't ape heteronormative dating customs. I don't pull my date's chair back, I don't help remove their jacket, or otherwise. (Unless they actually need help, of course.)
Because I do find these "chivalrous" gestures to be a little toxic. Given their origins.