And, for those who might be curious or simply don't know, the three times it's acceptable for a man to go or walk ahead of a woman (per gentlemanly etiquette) are:
1.) In a revolving door, so you (the man) are pushing it.
2.) On an escalator or stairs, so she won't worry if you're looking up her skirt.
3.) When entering a taxi, so she won't have to slide over or hike up her skirt doing so.
Do I dare provoke a Miscellaneous Double Whammy by discussing the treatment of women in a tipping thread? Hmmm, I think I'll go for it. And if things work out, I'll toss in discussing circumcision and declawing cats to really tempt fate.
Anyway, that's pretty outdated and kind of insulting (I know that's not your intention, 005
, so don't take it as a criticism of you, just the rules themselves).
1) It's polite to hold a door open for anyone, male or female, as long as you're not one of those jamokes who holds it open for people that are still forty feet away from the door, thus forcing them to do that awkward half run/half walk to get to the door faster lest they feel judged for taking their sweet time to reach the door they never asked you to prematurely hold for them in the first place.
But revolving doors don't have the same rules. Your only concern with a revolving door is making sure you don't get in a comical impasse with someone coming in the wrong way. Revolving doors don't weigh four tons and require a lot of strength to open like Victorian times, and the idea that women need a man to get the momentum started on the door because they're too dainty to push it themselves is equally outdated.
It's better to just let people go through in whatever order they reach the door, and let them set the pace for pushing it so you don't rush anyone through or slow them down. If you walk up to the door at the same time, sure, go through first. It doesn't really matter or call attention to anything. But if you rush past a woman to make sure you lead her through the door it will look like you're implying that she would have difficulty pushing it herself, and that's just insulting rather than "gentlemanly" or polite.
2) Maybe it's just my tall man's perspective, but it seems to me that you'd have to be standing pretty far behind a woman on an escalator or stairs in order to be able to see up her skirt (not counting those pervs who take the upskirt photos with their cellphones held near the ground) anyway. Unless she was in the WNBA star in a miniskirt and you were a Hobbit, it would seem that we would have to require pretty large gaps between people on the stairs or escalator for this to even potentially become an issue, in which case you should just not be a letch and don't stare. Waiting until a woman has reached the top of the escalator or stairs before the next man starts up seems awkward and calling attention to someone again.
If you're a woman's friend or companion and you're protecting her from the thought of you staring up her skirt, or she thinks you're the type of person who would do that yet is still hanging around with you regardless, you two have bigger trust issues to deal with.
3) What kind of douche is the first person to enter a cab but doesn't scoot down to the end of the seat and makes everyone else maneuver around them (or walks around to the rear door on the driver's side if traffic is light and it's not locked)? That's just rude all around, regardless of sex. If you're headed to different locations you should have the person who's leaving first sit closest to the door(s), obviously, male or female, but they should also be the last to enter the taxi.
ETA - Of course, as I was in the middle of my post I had to go take care of something, so when I came back and submitted it there have been a bunch of posts in between where people feel differently than me. So, what do I know? Everyone reacts differently.