Is it sexist to open a door for a woman ?

It is more sexist to ask the question in that particular way.

When she's carrying something in her hands, it's not sexist.

What if, at the very instant I hold the door open, I identify as a woman?

It is sexist - the way I do it: I see a woman approaching wearing a skirt and I lie on my back

This question reminds me of the episode of "Curb Your Enthusiasm" where Larry doesn't hold the elevator door open for a woman that he thought was too far away - only to be introduced to her in the meeting he was going to.

Well I’ll hold the door open for anyone coming behind me but I’ll only go out of my way to open a door if it is a woman, someone disabled or carrying something.

What if a trans woman holds it open for a trans man?

I call it proper manners.