"I agree with those who say that a gentleman (or gentlewoman, to use a less-used word) will open a door/carry a bag/help someone with a pushchair up or down stairs (and notice I say someone, not a woman). It's just good manners."
I agree that anyone should hold a door open for anyone else who is incommoded and unable to do it for themselves - by a pushchair, heavy load, etc. Men, women, children - anyone who is able should lend a hand.
What I object to is the idea that men are particularly and peculiarly obliged to do this because of an etiquette that, as far as I can tell, was necessary in an era of huge hoop petticoats where women were so ridiculously attired that they couldn't even reach a door, but is no longer needed in an era of more slimline clothes.
I have an acquaintance who goes to exaggerated lengths to show 'chivalry' - leaping out of chairs when women come into rooms, holding open doors for them. He also happens to be a patronising git who treats women like they are more stupid than he is.
When you come to a door, the reaction should be natural - the person who is closest and best able to open it does so. It's rarely an issue if you know how to occupy space confidently, and don't hang back waiting for obstacles to be removed from your path to walk along it. I will open a door for a bloke if I am closest and don't have a heavy load, a bloke will open one for me vice versa.