If it's about equality, why call it feminism? Why not call yourself egalitarians?
The great thing that comes with absolute clarification like that is it serves to properly expose misogynists and sexists, removing the ambiguity and leaving it blatantly clear that if a person says they're against it, they're stating that they are anti-equality. No more muddy waters.
I say, ask for what the actual aim is, and call the group/movement something that accurately fits the aim, and is not context/era sensitive. Feminism is a context sensitive term. When it came about, it signified the need to address rampant and blatant inequality. In a hypothetical world, completely dominated by women though, context would dictate that feminism would effectively be an attitude of a constant thrust to keep the "foot on the throat" of men. "Women's rights", on the other hand, simply asks for women to have their due rights. In that world completely dominated by women, woman's rights might be an odd thing to champion, but the meaning wouldn't have changed, since it's not subject to context.
So, it follows that men's rights, in name at least, is a different animal to feminism. Sure, one can say feminism but think equality, but do we really want that ambiguity? I see no valid reason to use feminism over egalitarianism, so I'd be left thinking that there's really just stubborn or anti-equality attitudes left to characterise the people that insist on it's use.
Weird example - If the Earth did indeed have a problem with global warming, and global-cooling-ism sought to, and could, address it, there would be a point in time when global-cooling-ism would become a negative force. Global-perfect-temperature-ism however would not be subject to the same fate. Just as the aim shouldn't be making the world cooler, it shouldn't be making the world better for women. They might be the action plans, but they shouldn't be the actual aims.