Chivalry is just another way of making out women to be weak and not able to do things for themselves.
and
We should all, men and women, be mindful of those around us who are less able to do things
Are women weaker and less able to do things than men or not?
I don't understand why you are connecting the two? I think the idea that men have to open doors (representation of chivalry) for women is based on the idea that women are weaker and need to be looked after. I didn't say that's my belief.
Which is why the second part stands too. Because we should all be mindful of those around us. Humans are social animals.
I always claim to be a 2nd waver. But actually I'm a pragmatic feminist. I can't lug sacks of coal around all day, but I'm not too weak to carry a box of paper upstairs, along with all the other members of my team, when we get a delivery and the lift is out of order. But everywhere I've worked, the men have been asked to do that and the women not. I am no better at setting up a meeting room and making coffee than the next person, but everywhere i've worked the women have been asked (expected) to do that and not the men. So for the paper, i jump up and grab a box. For the coffee? I find an intern, and i alternate between the male and females, because we can all do that.
etc etc.
But i don't want some guy pushing forward to open a door for me just because I'm a woman. I can open doors unless i have my hands full, and then i appreciate anyone who gives me a hand.