I don't think it should be called 'Chivalry' anymore, because 'Chivalry' was a code of conduct for knights who were noble-born. It DID include courting women, but there was a lot more to it.
It should be common courtesy for EVERYONE, regardless of how they identify or what's between their legs. Men don't feel like they should have to curry favor with someone by doing a bunch of silly things and spending money (IE free food/drinks to the person they're interested in). If you like someone, strike up a conversation with them.
Being polite is fine, and I wish everyone was. I hold doors for everyone but I don't expect anyone to do it for me. Personally I try to avoid situations where some guy will hold a door for me just because he was 'taught that way'. I wish people would stop teaching their children to be 'chivalrous gentlemen' and instead teach them the value of respect and kindness to EVERYONE they meet until an individual gives them a reason to not be (a rude person refusing simple kindness is the best example).
I often feel like people who get priority to go first through doorways are generally older than me, have their hands full with groceries/etc, have young children that they need to hold, hold hands with or push through in a stroller etc, or just someone who seems to be going the same way as me.
Women are right to feel like it's sexist when they see a guy who ONLY opens the door for women, but not for the guy behind the woman, etc. That IS wrong and should be stopped.
But then again I've never cared at all for a lot of social practices. I don't want to be pandered to and patronized because of my genitals, I just want to be treated like a human being. I feel like everyone else should want the same things, but I'm not going to make a public outcry because someone likes the whole 'Gentlemen and Ladies' social play; I just don't agree with it at all.