Okay, this is probably ASB, but somehow, have feminism get stuck in its 80s/90s rut, where its perceived as being focussed on things like banning pornography and pursuing dubious cases of Satanic Ritual Abuse. Maybe the MacKinnonite Minneapolis ordinance passes, which emboldens the antiporn crowd to continue trying for similar legislation elsewhere. Even if they don't have much success, just keeping it going as an issue will probably cause feminists to wear out their welcome pretty quickly.
(Sorry, I don't know how you keep SRA going, since there are only so many individual miscarriages of justice that you can have before the public starts to connect the dots. But anyway, let's assume that feminists, at least, decide to keep making this an issue...)
So, after a few more years of feminists sounding like a cross between Carrie Nation and David Icke, the public is thoroughly fed up and ready to embrace any movement that promises to stop them. Though, honestly, if that did continue to be the main current of feminism, the movement would probably just die from public disgust/indifference anyway.
And on the Men's side of the equation: Have more people care about whether or not custody cases are fair to men(which in my experience is one of the driving issues of Men's Rights). As it is, people might get upset when they hear about some guy they know getting shafted on visitiation rights or whatnot, but they're pretty indifferent to it on a societal level. I'm not sure how you go about getting people to care.