Its about power and control.
Look at who wants to be the gatekeeper and why.
Females being the gatekeepers to women makes sense.
Males trying to dictate to women who gatekeeps women shows you the nature of the problem
Being inclusive is a weasel word in this context.
Reflect on what is the objective of that single sex space?
For women its about giving opportunity there otherwise would not be, privacy and dignity reasons on a biological level and safety reasons.
The converse does apply to certain things for men - for example the dignity element kicks in for health care and states of undress for biological reasons. You also have socialisation issues, so for example an all male mental health group has a legitimate aim to enable men socialised to be 'the man of the family' to off load without the responsibility they feel they are supposed to carry. And you have the safety reason element in sport, because males don't really want to compete against others they are likely to cause harm to (this relates to weight, age AND sex).
What is the objective of a women's only knitting club? To enable women to gather and socialise free of males dominating the conversation because of socialisation and allow them to gain social confidence.
What is the aim of a women's climbing club? To enable women to gain confidence in the absence of males, to be free of comments about their physical form or attire and perhaps learn techniques that are particularly helpful for women's strength to weight ratios. And again to encourage them to do a sport that often women will self exclude from due to a fairly macho culture.
If you add a male to either of the above, you end up with women self excluding and you defeat some of the aims and purposes of why women set up those groups in the first place
This doesn't mean there isn't a need for transwomen/transmen to socialise and feel they have their own space where they feel free and that encourages participication. Its just that their needs to enable participation are in conflict with those of women. Instead they actually need trans groups which are dedicated to pursuing aims which are not going to lead to self exclusion elsewhere.
Single sex provision is ironically very often about promoting participation in society as a whole rather than separation from it. And thats the really notable point.
Thats also where single sex old fashion mens clubs can fall apart - if they ultimately aim to exclude women, rather than addressing other issues such as for example male isolation - which as an aim SHOULD definitely be a goal.
Gender replacing sex, loses sight of certain things, as does going 'gender neutral' which often isn't neutral at all as it actually favours men as the default human.
A gendered group is reinforcing sexism because you can't define gender without using sexist reference points to stereotypes. An undefined criteria 'in your head' is unenforcable because its too easy to open abuse.