I'm against sexism, double standards and biases against women (and for all kinds of discrimination for that matter). Women face a lot of issues: sexual abuse, unequal pay, objectification (which also happens to men, but not to the same extent), domestic violence.
It's great that women get more into the leading roles in movies and sports so they can be real models for the young girls and teach them that they can become anything they want, that they're just as important as men. I really appreciate men who do enjoy and support women in those roles, but I think it's not sexist of me that I don't. I guess it's a matter of empathy, I can't really identify with them.
When I see a strong and handsome rugby player I can identify with him: that could've been me if I was strong and handsome. If I see an interesting male character in a movie I can identify with him: that could've been me if I was an interesting person. But that does not happen with women. And for this reason I understand why very few men write scripts where women have the leading roles. If I would think of a story with a superhero, that would be a hero that I could identify with: a dull and awkward guy with low self esteem and who's a turnoff for women.
And for the mandatory sexist joke: I only enjoy one kind of movies with females in the leading roles, if you know what I mean.