No, and to be honest, it's not something I plan to teach. Something about "Girls go first" makes me uncomfortable but I can't clearly articulate why.
I do teach my child to hold the door for others - if you are there first, it's polite to hold it for the people behind you. Or to ask someone "can I hold the door for you" if there is someone who appears to need help, regardless of whether the person is in front or behind you.
I teach him to let others go first if the other person appears to be in a hurry - maybe they have something going on that we don't know about.
I teach him to let others sit on a crowded bus, regardless of gender or age, because we are healthy and able to stand.
But no, I don't tell him that girls go first.
I am very curious about others' answers here, and if they do teach this, how they do so.