I would assume the man holding the door for me would hold the door for anyone else.>>>

A somewhat complex question is raised here, regarding conventional courtesies to which one has been brought up in conflict with expectations of full equality. I am an old man now [77], and young people will still sometimes offer me a seat in a crowded underground train in London. When it is a young man, I consider it civil on my part to accept with a smile and grateful thanks. But when it is a young woman, I explain that, tho grateful and appreciative, it would just fly in the face of all my condiditioning to accept a seat from a lady and beg her to resume the seat without being offended by my refusal. I will also offer my own seat to an older woman or one with children, but not to a younger woman.

I am unsure how these principles of mine would stand up to the scrutiny of GuestEmmaB.