While I think it's great that you're acknowledging that men face problems in our society as well, I don't think approaching them from a 'feminism lens' is the best way of going about it.
Feminism, since it's inception, has been a movement focused on bringing women to a place of equal standing with men in regards to rights and opportunities, and although it's seen many different mutations and evolutions over the years, it still carries that same basic principal at it's core.
Feminist Theory, the 'lens' I believe you're describing, aims to explain gender equality by examining the social roles and experiences of women. This alone makes it entirely incompatible with a group of men discussing men's issues unless (laughably), each man sent a women in his stead to discuss his issues from her perspective while he stayed home.
It becomes even more difficult when we add ideas like 'patriarchy' and 'male privilege' into the mix. We essentially get a situation where the problems that men are facing are either 'privileges' or 'their own damn fault'. Anything else and it begins to undermine and dismantle the very 'lens' we're attempting to view these problems through!
This already sounds like a terrible way to help men find a solution to the issues they face. My conclusion is that Feminism is entirely incompatible as an ideology to discuss the issues men in today's society face.
As much as it'll pain some people to accept, Men in countries like the US, Canada, UK, etc need the MRM right now. They need to be able to gather and discuss these things without worrying about fire-alarms being pulled, posters being ripped down, a wall of nearly violent protesters blocking the entrance, or a 'feminist presence' to police these discussions. I've found that the MRM in general is very level-headed and peaceful.
On 'Red Pill Thinking': While I can agree that the particular brand of TRP here on Reddit is extreme (and even that might be an understatement), I think the reference it uses holds some merit. By realizing that men face issues and that they need a safe place to speak about it means that you've actually swallowed a 'Red Pill' of sorts yourself.
Furthermore, 'Red Pill Thinking' is, more often than not, a byproduct of the things that feminism has changed in society over the years as well as the female biases in many aspects of working class society.
Even the most noble of causes can have unintended side effects.