I'd rather we point out "sexist behavior" to help make it stop vs introduce an even more subtler sexist behavior
In your senario: You, as a man, aware that she as a women, can get treated differently, so you will then treat her differently based on that.
You see, you are still treating her differently, where ultimately, no one treats her differently.
Reminds me of this quote from Morgan Freeman in an interview
Wallace: Black History Month you find...
Freeman: Ridiculous.
Wallace: Why?
Freeman: You're going to relegate my history to a month?
Wallace: Oh, come on...
Freeman: What do you do with yours? Which month is White History Month?
Wallace: Well...
Freeman: Come on, tell me.
Wallace: I'm Jewish.
Freeman: OK. Which month is Jewish History Month?
Wallace: There isn't one.
Freeman: Oh. Oh. Why not? Do you want one?
Wallace: No. No.
Freeman: Alright. I don't either. I don't want a Black History Month. Black history is American history.
Wallace: How are we going to get rid of racism...?
Freeman: Stop talking about it. I'm going to stop calling you a white man. And I'm going to ask you to stop calling me a black man. I know you as Mike Wallace. You know me as Morgan Freeman.