[All these points apply to sex and to gender, so for ease of reading, I'll just discuss gender]
Gender-exclusive groups are common in many societies, such as men-only and women-only social clubs and casual activity groups like a men's bowling group or a women's reading circle.
Sometimes this is de-facto, but sometimes this is enforced by rules or expectations, treating the club as a safe space for airing issues people have with other genders, or avoiding perceived problems with other genders.
I came across this old comment in a garbage subreddit by accident when researching. The topic is Men's Sheds:
"Here's the thing. No reasonable person has an issue with women having their own women's activity groups. The annoying part is that whenever men try to do something similar, that's a problem. Women either want them banished or demand entry, EVERY time."
I think their claim is nonsense, grossly exaggerated at best. I also know of many counterexamples of men trying to get into women-only groups (as an extreme case, the Ladies Lounge of the Mona art gallery in Australia was taken to court for sex discrimination, with the creator claiming they would circumvent the ruling by installing a toilet). But nonetheless, I can understand why they feel this way, patriarchal social relations change how most people see men-exclusive spaces vs. women-exclusive spaces.
But my response to their claim is that, I am reasonable and I do have an issue with any group setting up places which discriminate based on gender. These safe places can form as a legitimate rudimentary form of protection, yes, but they maintain and often even promote sexism, and should all be challenged and turned into something better which serves the same purpose.
Of course, I'm limited by my own experiences and perspective, so I'd love to hear your opinions on the topic.
Bonus video: "Why Do Conservative Shows All Look the Same? | Renegade Cut" - a discussion about fake man-caves and sexism.
My rpg club took the incdusivity road in the 2010, and is now a very inclusive/diverse place. We do have the blue haired enbies that riqht winger hate, and some old players who after acouple of beer starts complaining about RPG becoming woke (An inclusive place means they're welcome too)
We do have a couple of women only group and a point someone launched a men only table. While we had one of the old player complaining about the women only game, no blue haired enby complained about the men only game. So I have the impression that this whole women only space are OK, men only space aren't is some bullshit.
Note that, this worked becaused the gender specific game include people identifying as this gender, are the exception, and have a justification. It's not I don't like wo•man so I want only a gender but * I want a game exploring masculinity/feminity and therefore will limit the cast gender*
This is dancing around the Karl Popper paradox of tolerance, but it sounds like your RPG club would draw the line somewhere and kick out someone acting blatantly disrrspectful.
It sounds like in this specific case, men wanting a male only group would be in a minority, so it makes sense that women and non binary folx wouldn't feel disturbed by that. Vs. a men-only bar that all the business people go to or something, where exclusion would be the group in power enforcing their power.
That last sentence hits pretty hard. Like why would anyone want to be involved with something they don't understand and/or care about?