Well they should be fighting the same fight. It's too bad MRA exists in spite of feminism
So, "Why does it exist in spite of it, and what can be done to bridge the gap between the non-crazies on both sides?" should be a discussion. Instead, it always devolves into name-calling.
(Note: in the following section, I am not trying to false-equivocate anything, I'm very aware that the sum total and seriousness of the issues facing women vastly outweighs those facing men.)
The fundamental problem is one of perspective, self-interest, and a lack of empathy on both sides. We respond strongly to negative stimuli. Men see problems in their lives, things they don't like, and they work for ways to remedy the problems they see. Women do the same, looking specifically to remedy their issues. These movements attract people who feel aggrieved, victimized, etc., by forces outside their control, and who specifically want their interests to be taking center stage.
This leads to conflict. Often people aren't able to step back and look at the broader whole to understand where conflicts are coming from. The world is not one monolithic layered pyramid, where there's a clear upper class, and you can just point to a chart to find out where you stand next to someone, because everything is contextual. Men are privileged in many ways over women. However, in some situations, Women have privilege that men do not. Sex, Gender, Race, Nationality, Sexual Orientation, etc. - these all work in an interlocking fabric that manipulates the way our lives play out.
But backing up and trying to see a top-down aerial view of these issues appears to be incredibly hard for people, let alone trying to use empathy to try and imagine themselves in someone else's first-person view for a day. I do not think it's an accident that the most frequent blow-ups occur regarding sex. Men and women do not experience the world in nearly the same way, and have different ideal "endstates" for what their ideal world would look like in that regard. Tremendous resentment builds up due to each of them desiring the other half of the species to act like their half instead, leading to a blow-up each time we have a topic about eye candy in video games, how straight guys communicate on Tinder, or how men are deeply frustrated by a lack of sexual contact.
And so we see the camps divide, each feels as though its being attacked by the other and not taken seriously. People segregate, much like a HS lunchroom, not able to talk to each other about serious issues, because when one side expresses how it feels, the other dismisses it off-hand as being "stupid" or "wrong", even if its simply a feeling, which isn't "wrong or right" - it just
is.
I don't know what the answer is to try and fix or bridge this. It feels like we're doomed to repeat this cycle, because people simply can't break out of their own experience and self-interest and trust that many people are actively being honest, instead of trying to insert their own values, experience and emotions into someone else's head and tell them what
they would have done. There's so much stuff that shouldn't be controversial to fix in the least that just gets left undone because people can't trust in neutral data or each other.