I am afraid that a lot depends on cultural context of the whole society. I don’t think the context is fertile for men’s activism for rights. The groups that exist are almost exclusively misogynist and conservative. I believe that a movement, even if really focused on men’s issues from a general perspective (I.e. not misogynistic) would be received very poorly, will fail to develop solidarity with other groups and would be accused of stealing space to them.
Frankly, I am not convinced at all that each demographic should fight their own battles, I believe in better analyzed demands that will merge under the same front gay rights, women’s rights, men’s rights and so on.
I mean I exist in a very LGBTQIA+ city. My friends across the spectrum of the rainbow have expressed sentiments about how men’s mental health is an issue but it is really hard to interface with it because men like to talk about it… but they seem to want to nope out of and defer spearheading an initiative. Because it’s not easy. It never is easy.
Most of the LGBTQIA have a model. A group who is directly plans a thing and then the people who are adjacent show up. People generally have the spoons to make one to two issues their main. This is usually where they take the effort to spearhead the thing, be part of the committee, figure out the logistics and run the getting the word out. That issue because it is so energy intensive usually is one they feel most directly affected or endangered by… but they can make time and energy to show up for like 10 other things to do fundraising, protests or whatever because they support friends. Stuff where they just need to know where to be and what to do. That’s comparitive low energy.
You could look to the LGBTQIA as help and go to like a Pride committee but generally speaking when approaching people for help you have to expect imperfection.