Both movements suffer from a collectivist us vs. them mentality. To MRAs, men are forced to risk life and limb to protect those privileged women. To feminists, women are being oppressed by the misogynist patriarchy. Things aren't actually that simple though. You can't just say that men/women are oppressed, and pin it on some ideological boogeyman. Men and women both have problems that they have to deal with. It's much more effective to look at the individual issues than to wrap everything up in a religion.
Just because the movement doesn't solve every problem or explain everything doesn't mean it's not useful. Of course things aren't as simple as men this and women that however there are still issues that can be worked through using feminism. There is plenty more to feminism beyond men/women are oppressed but you have to actually look for it.
What I'm trying to say is, you can have a movement that advocates for something without being ideological/dogmatic. A big problem with the MRM and, even more so, with feminism is that they cling to ideology, even when they are proven wrong.
I can't say much about the MRM off the top of my head. An example in feminism is the gender pay gap. Itdoesnotreallyseem toexist. At least not in the way most feminists think it does. Yet people still go around claiming that women earn 77 cents to a man's dollar.
I've heard a lot of different views on the wage gap some with more merit than others, but really there's no way to get rid of misinformation in any subject. For example science, or politics. The thing about feminism is there really is no governing body saying what's accepted as there is in some sciences. There's no "Bible" either as there would be in religions. It's really not regulated at all which I think was a good idea in thoery but really doesn't work in practical terms. It's a giant clusterfuck actually which is why I don't really get the comparison to ideologies or religion.
There really isnt even one bible. There are multiple translations and an infinite number of number of interpretation. Feminism at its core is about equality for women the same way that Christianity is about the bible. After that it's up to the individuals interpretation, does it mean mandated equal wages? Does it mean special rights for women that are in place to fight years of inequality? Does it mean that men should shut up and get back to the kitchen and have no property rights for the next 2000 years to counteract all the previous oppression . All of those could theoretically mean equally just like all sorts of shit can be interpreted from the bible.
It's impossible to look at issues alone because they all intersect. My womanhood is not just about being a woman. It's about being queer and Jewish as well and the meanings that are ascribed to me because of that.