I've got dozens of things to say about feminism (both pro and con - mostly pro) but will address just this one matter you mentioned:
For years I, like you and others, was always taught "ladies first". We would hold the door for ladies, serve them first in wine and cheese parties (I no longer drink alcohol), and allow them to step onto the city bus before we did.
Then a big social change occurred: many Southeast Asians and East Africans have moved into this area. In those cultures it is always
men first, ladies second. For the past couple of decades now whenever I hop aboard a city bus and there is an Asian or African lady they step back and allow me to enter the bus first. One Abyssinian lady (these are Christian East Africans) went so far as to make a full bow in my direction before I stepped onto the bus! I was startled at her incredibly respectful manner.
Well, just a couple of weeks ago I was at the bus stop and chatted with a white lady from this area. I gestured for her to enter the bus and she did so before I did. Gosh - what a feeling it gave me for her to allow me to act like a Western gentleman again.
Yes, I know times have changed and with the ever increasing Muslim/East African and Southeast Asian populations that we see in this society, eventually things will likely change to the day when it will be universally
men first. This may come about sooner than you think!