You're not thinking like someone born in that era. Sisterhood-and-liberation is a familiar idea to us because it pervades our culture, because it was inspired by previous movements and ideas, which probably haven't happened in this world.
Yes, SOME women will believe that women in general are more capable than the patriarchy claims. But at the same time there are going to be many who are content to be recognized on a personal level, and many more who will seek to emulate the former. Likewise, they aren't gong to be "shit on" for being women unless they seem to be getting subversive ideas into their pretty little heads.
What we're ultimately dealing with here is a cult of pragmatic optimism. Society wants to recognize people who get shit done, so women doing 'mens work' will be patronized but still encouraged.
"Aww, you wanna try? Here, let me come up behind you to show you the controls from the spoon position. I know, it's complicated, don't feel bad if you don't understand it honey."
, or "Jesus, I ain't never met a dame who could drive like 'at!",
or my personal favorite, "HA, excellent idea! By golly sometimes you think like a man!"