If a man runs or sprints to get ahead of an unencumbered woman to open the door for her because she is a woman, he is acting condescending. That is rude not mannerly.
If, when approaching a door through which you plan to go and notice someone coming from the other side or coming from behind you, it is good manners to hold the door open for them whether they are female or, imagine it, male. It is not a sexist act. It is not some kind of “come-on.”
Most women know that and will not only not be insulted but will appreciate the courtesy.
I’ve had the door held for me by women and men when I was still able bodied and always appreciated it and never felt insulted.
I thought we were past that sort of hypersensitivity. Sexism still exists in pay inequity and access to promotion. Those are important issues, but not who hold the door for whom.