I asked a Godol and he assured me that the Gemora’s statement that a man should not follow a woman most certainly does apply to a situation where the woman walks through a doorway, as it is clearly the case that the Shulchan Aruch rules on.
The Gemorah (Brachos 61a & Eiruvin 18b and see Rambam Hilchos Isuurei Bi’ah 21:22, Shulchan Aruch E.H. 21:1, Aruch Ha’shulchan E.H. 21:2, Otzer Haposkim 21:16:2, Sheilas Rav 1:16:4) states that if a man and woman simultaneously reach a narrow passageway the man should go first since it is improper for him to walk behind a woman. The Gemorah then adds that this Halacha applies even to a husband and wife, and Rashi (Eiruvin ibid. “afeilu”, and see Aruch Ha’shulchan ibid, Tzitz Eliezer 9:50, Divrei Yatziv E.H. 39, Sheilas Rav 1:16:5.) explains since it is unbecoming for a husband to walk behind his wife.
The Histaklus B’halacha 4:16 specifically says one cannot walk on a bus behind a strange woman (i.e. not his wife). According to various psakim one cannot even sit behind a woman (Chut Shuni Tznius page 50 quoting the opinion of the Chazon Ish, see Oz Nedberu 10:28, Kovetz Halochos for The Summer page 52:footnote 18).
And the reason I cited that al pi Torah you save a man’s life first, was to demonstrate that the goyish etiquette of “lady’s first” is Keneged HaTorah.