>> And you are conflating anti-feminism with misogyny.
No, I'm not, in fact I'm explicitly and deliberately not doing that, as I said here -
"I'll concede that a lot of outspoken feminists often try to intentionally confuse this issue as well, painting anyone who disagrees with any facet of feminism, no matter how extreme, as being misogynist."
>> Feminism can't be natural ally of mens' rights because it is actively pushing against it.
I disagree.
--edit--
In fact I disagree entirely, there's no reason at all that a mens rights movement could not exist to push the issues you call out, and work alongside a feminist movement working on feminist issues. Women campaigning for greater access to the workplace, and against street harassment, are not in opposition to men wanting greater access to their children. This is what I mean by natural allies.
The idea that they are necessarily in opposition is childish.