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retro; When you say "doff" do you mean touching the brim, lifting it slightly, or removing it?
I'm pleased none of the women on here have said it was patronising.
I think you must always remove a hat (men) when entering someone's home but some areas are ambiguous, like this morning I called in at my dentist's to make an appointment, didn't remove my hat in the corridor, but did so at the counter before talking to the lady-receptionist.
There seems to be less & less men wearing hats nowadays anyway.
There is a TV Scottish reporter, I think on Sky News, who has a rosy & round shaven head & he gives reports even when it's snowing without one, whether that says something about modern man or the Scots I don't know.
Look at an old outdoor photograph & you won't see any man without a hat or cap.