Well, yes, technically.
But I won't lose sleep over it, and I prefer to show manners myself. It costs nothing.
I will not usually extend a courtesy to someone who demands it and is rude though.
I also believe that ettiquette and manners must be expected from women, just as much as from men.
Can't say I am surprised at the thumbs down. Ettiquette is not supposed to be a systemof rules and manners imposed on men and soley for the benefit of women, as many here think. I have very good manners, but I will always refuse some of the finer points of etiquette to those who seem to think they have a God-given right to be treated specially. These people, at least in my experience are also the loudest when shouting for women's rights.
I would also add that comparing ettiquette to racism is not in any way a true comparison. Racism as you describe was enforced. Ettiquette rarely is today, beyond a few basics.