I'm also a gay man, and just to preface.

While the two groups clash due to characteristics of their followers, in a perfect world both MRAs and feminists would be able to accomplish their goals simultaneously. Much like feminism, rational MRAs want gender equality on all fronts. Just because you might find the causes of one group to be more important than the other doesn't mean that the the causes of the inferior group are invalid. Feminism has extremists just like the MRA campaign does, but feminism also has a much larger network that allows for more diversity of opinions (a spectrum, if you will). I will agree that I see MRA being more on the extreme side overall, but there's a reason for it that I'll address below.

On a human level, people are more sympathetic to causes they identify with. More women are feminists, more gay people are involved in the gay rights movement, etc. It's human nature that if you feel like you are constricted in some way that you would want to change that. While you could argue that some of the issues facing MRAs are much more inferior to other groups, it should make sense that men would want to change issues facing them.

As a gay man myself, you should know how toxic the current state of masculinity is. It kept me in the closet much too long, and I treated women poorly in order to sustain a certain social status. Even in the gay community, "masculine" gays are revered and more attractive. A big underlying current in many MRA issues (male rape, suicide, etc.) is that men are too afraid to talk about certain issues because it makes them vulnerable.

This toxic state of masculinity could easily be argued as a catalyst for many women's issues and gay issues, as well. You can look at the Red Pillers and see that these are young men who were raised to believe they are deserving of female attention as long as they go out and get it. When that doesn't work, they go to more extreme tactics.

Back to my original point as to why the make-up of the MRA movement is more extreme, and this is conjecture. This get the fuck over it mentality is exactly what would constrict men who are less extreme to join an MRA movement. We are supposed to have our shit together and not show vulnerability, and being associated with a MRA campaign would show exactly that.

Just to dig further, promoting gender equality on all fronts seems like the best method of eliminating toxic masculinity from the equation, but a big reason that the MRA campaign has sprouted is because feminism is not tackling this issue head-on. Who else can fix toxic masculinity but those who suffer from it?