I generally agree with all you've said there. I guess I have so much personal experience with non-sexism prejudice in all kinds of ways that I don't really care about the plight of women as much. It seems like everyone gets it. If someone asks as question on StackOverflow, I judge them for having a default avatar or username. I judge them for having a teenage writing style. If someone writes in 3rd person or 1st person, you can judge them in either direction depending on whether other signals are consistent with it. I try to combat that in myself and treat everyone fairly, but ways to judge people are just overwhelming even without knowing their sex. You get judged by the way you walk, the way to look at people, the timing of your speaking, your age, your clothes, everything. You might say those features aren't innate and people can change them, but it can be incredibly hard for some because they're actually signals of some underlying qualities and if you don't have those qualities, you're struggling to fake the signals which is risky and difficult.
I think women may actually get a better deal overall because so many men are trying not to be sexist that they treat them well, giving them a free pass on all those other judgable signals. Men might not even understand that a woman is revealing her inadequacy by wearing the "wrong" clothes, while they'll openly laugh at a man exhibiting "wrong" behavior.