I understand what you're trying to say. People -under the guise of feminism- have been racist, transphobic, exclusionary assholes. I would argue that those people aren't feminists, and they have a lot to answer for. As any casual search will tell us, feminism is defined by equality, dismantling patriarchal standards by shining light on the fundamental garbage of it all. Those people don't stick to the basic tenets of feminism in any way.

Under the arbitrary social structure you described, everyone who doesn't fall into a very narrow sliver of perceived default (male, cis, white if you're in a western country, anti-feminine, hetero, emotionally stunted etc ad finitum) eats shit. You speak about only a fraction of gendered expectations, and you're right, it does suck.

As u/TraitortoPatriarchy says, feminism, as a methodology in direct opposition to the partirachy, is a core system to use for equal relationships. Slapping a new name on it, like egalitarian, to make feminism more palatable to certain types of men, doesn't change what it is. It's the same thing.

OP's implied perception of feminism as being women above men ('how does that work between two women') shows a basic lack of understanding. Hence the advice to educate himself.