From an outsiders perspective as a female, it definitely seems like men get a lot more hate for not being masculine than women do for not being feminine. I have never really been anything close to "girly," but I have never had anyone say anything negative about that aspect of me. When I was little I hated the color pink, barbies, my little pony and pretty much anything "girly." While nowadays I am a little more willing to indulge in things that are considered feminine, like My Little Pony, I would still much rather play video games than go shopping.
Men, from what I've seen, cannot do this. If a younger boy plays with dolls, he is derogatorily called "gay," which is unfair both to the young boy and to the LGBT community. It seems like if a male deviates even the slightest from the masculine stereotype he risks being bullied both verbally and physically. Sometimes a boy doesn't even have to act more feminine, it can just be a physical attribute, like their voice, being more feminine and they are mocked for it. I feel like while the focus of sexism is predominantly on that against females, there should be a lot more focus on sexism against males.
In an earlier post it was mentioned that in a way girls are rewarded for breaking from their stereotype whereas boys are punished for it, and I think this is a very interesting point of discussion. If a woman is a nuclear engineer, people will think, "Wow, she's an independent, strong women who managed to elevate herself above the sexist stereotypes. You should look up to her young girls, because she is an amazing person." While this is a good standard for society, the contrast to the opinion society adopts when a man takes a more "feminine" job makes it seem almost derogatory towards men. If a man were to become a ballerina, then societies standard viewpoint is, "Don't be like that boys, you want a more manly job, like something in engineering or construction." Now not all of society is like this definitely, and I like to think that a large percentage of it is more accepting than this, but this seems to be the general vibe I seem to get from the society around me.
I apologize if anything I say has offended anyone. If anything I have said seems inaccurate, this may be a result of my living situation, because I have spent my whole life in a highly conservative, highly religious state and in a highly religious, highly conservative family, so any views on society I have presented may not be an accurate depiction of society as a whole, but rather of the society I live in.