I think the real, insidious and yet somehow acceptable sexism is the very idea that men should feel obligated to open the door for you in the first place.
You demand men try harder to see your point of view, while almost entirely ignoring theirs? For a tiny, brief moment, you felt some of the obligation men feel when they’re expected to open doors, pull chairs, take coats, stand in your princessly presence, remove any hat, pay for you, protect you, even die for you, because you know, genitals?
And the obligation, the ‘sexism’ you felt, was a slight annoyance at actually having to make it a bit easier for some random guy to service your female pampering?
Physician, treat thyself.