"Egalitarian" is the word you're looking for. Which means that you acknowledge and oppose unfair treatment for anyone, whether from reasons of sex, race, religion or sexuality.
It's been shown that from almost Day One, nurses tend to pick up and cuddle babies in pink more than ones in blue: boys are supposed not to need comforting. This is why men classically have problems with expressing emotions, getting close to their children etc.If life treats women unfairly just because they are women, it can do the same to men. Men can be just as much victims of the so-called patriarchal society as women are.
My sister has a sign on her kitchen wall saying "I'll be a post-feminist when the world is post-patriarchial."But I have to admit, I don't quite get women who claim there is no relevance in feminism or who revile it. One only has to look around the world and see the powerless, uneducated, grinding struggle that is the lot of too many girls/women.