ps to above post: I just reread my above synopsis of Rav Frand’s shiur which was written right after I listened to it, and he quoted Rav Shlomo Zalman as saying that in any situation in which manners dictate letting the lady go first, the man should do so.
So, we do believe in manners, and we do believe that men should let ladies go first when it is dictated by manners!