Is there something wrong with good manners now?
It's never rude to open a door for anyone, male or female. Whether or not someone chooses to make a big deal of it is a fine indicator or exactly how petty a person they are. If I keep you on low wages just because you happen to be a woman, I'm a chauvanist pig and I deserve to be treated as such. If I open a door for you, be grateful. If you open a door for me, I certainly will be.
If you think little things are just symptoms of bigger things that's fair enough . But opening a door? Getting agitated about something so minor is the sign of someone who has too much time or too little sense of proportion.
A good case for equality - which is a fine thing - ruined by stupid overreaction.