Putting a urinal in a men's restroom and not in a women's restroom is not sexist, even though they are being treated differently based on sex, because there is no prejudice or unfair discrimination going on.
The handshake rules are not necessarily prejudicial or unfairly discriminatory. Some of them might be, some of them might not. It's best to think of sexism, and other isms, as a spectrum, and not hard and fast rules.
I tend to hold the door open for people (male or female) if they are following close behind, or if I'm exiting just as they are entering. It's a subconscious thing that I don't think about before doing it.
Occasionally, I get a sneer from women. I assume it's an assumption on their part that I'm being sexist.
That is what I do in the situation where someone is following close behind. Again, reflexive, not conscious...would be hard for me to change it. To be fair, I don't really know the reason for the occasional sneer. But it is almost never a male sneering.
The handshake rules are not necessarily prejudicial or unfairly discriminatory. Some of them might be, some of them might not. It's best to think of sexism, and other isms, as a spectrum, and not hard and fast rules.