Are you saying that I could open the car door for a man and pump his gas, because honestly I would never do that. I agree that chivalry excludes same-sex couples and nonbinary couples which is why some people expect each person to take on the role of a gender, man or woman, even in same-sex couples. I think that is highly problematic and insulting.

Yes, the person who asks for the date should pay, and who pays for what as the relationship progresses, is going to be dependent on who has the most money. If the man thinks it always has to be something, like a trip, that he can afford, it's going to be a problem if the woman has more money, and wants to do things that cost more.

Yeah, I don't agree with gender essentialists, and yes, a lot of people think the man should always pick up the tab, hold the door, etc. because he's a man. And no the nature of the relationship doesn't matter. You can't force people to believe or behave this way.