[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.