edit: I just realized between those comments I said the modern men' rights movement is both equivalent and not equivalent to modern feminism. What I mean is, they're equivalent in the way apples and oranges are both equivalent as fruits. They fill the same roles but are otherwise entirely different.
And it's ironic, because the mens' rights movement coined the term "toxic masculinity," and it has its roots in traditional masculine/chivalrous ideals and teachings, but now modern MRAs consider it to be nothing but a slur. It's like masculine culture becomes more defensive the further feminism encroaches into its traditional domain.
Indeed. That was very much my original point. I've thought about trying to start one. But the prospect is rather daunting considering that unless done very carefully, it could well end of offending both feminists and MRAs. Which could lead to some... interesting experiences.
Note that feminists mostly encourage many of those traditional gender roles, which is why male movements needs to go against feminism. For example when men opens up about problems women screams out about all the "emotional labour" they now have to do, they don't want men to open up they just say they do to look good and those women are the main reason men actually aren't opening up.
However, one thing here, many male movements has given up on actually fixing the problem and instead focusing on what the individual can do. So instead of trying to fix women, they just accept that women will never see them as humans and work around that. Which is why you get MGTOW, the incels, the dating players etc.
Edit: Also note where we put the blame here. When women creates groups encouraging each other to lose weight and become anorectic, do we blame that group? No, somehow we blame men who wants women to not be fat. However when men creates groups trying to adapt to the insane ideals women puts on them we call it toxic masculinity and blame men anyway.