Oh, ballet participates hugely in gendered stereotyping in performance stories, and has done from its inception. But there's an interesting twist: in Giselle, for example, the typical boy & girl romance, but boy is really prince in disguise, falling in love with a simple peasant girl, dumps her, she goes mad & dies. That's the first act. So far, so 1841.
But in the 2nd act, the Prince seeks out the spirit of Giselle, who is now a Wili - one of the ghosts of girls who all died from being spurned by their lovers. They seek out men & pitilessly dance them to their deaths. Revenge by pointe shoe!
In a standard professional class, the men & women all dance together. Towards the end, the men will do different jumps to the women, and the women will do different turns. When I go to an advanced class (less & less often at my advanced age), we all do the same thing, but the men/boys are encouraged to add stuff to their jumps, or the teacher will give them a different ending to a combination of steps.
But I've learnt all the same steps and same jumps. I remember one class I used to go to when I lived in the US, and there was a guy in the class that I'd race with across the floor. Jumping with the men teaches you how to get their speed & lift.
And here's a man in pointe shoes:
All these fake transsexuals start to make good ol' male drag queens look somehow wholesome, even though the whole concept of drag is historically based on misogyny.