Sadly, I think this one has started to go out the window because of women more so than men. A lot of women in the ultra-feminist movement find door opening to be offensive. They believe it implies a the man doing it thinks the woman is too weak or too dependent upon others to be able to open her own door.
Personally, I feel who ever gets to the door first should just hold it open. It would be pretty rude and audacious for the woman to arrive at the door and stand there, waiting for her man to open the door.
Though, it’s something I can definitely picture my late Nana doing! 😅