In terms specifically of men joining women's groups I sort of have experience of this
I belong to a heritage craft group that generally speaking tends to be something women do more of but historically the group has always been open to everyone
Over the 30+ years I have been going I can remember 3 men attending at different times.
The first two were extremely assertive to the point of aggression, they both managed to get elected to the committee very quickly and then bullied the other members of the committee to the point of tears on more than one occasion. I can remember horrific committee meetings and AGMs that still get talked about now 20 years later where red faced men yelled at women because they wanted to be heard and be the most important and vocal person in the room.
Currently we have one man in the group, he's fairly quiet and fairly happy to stay more in the background but I will say @EndlessTea had the best description of the dynamic
I have experienced a man in a women’s group and the women’s behaviour changes. It becomes a male-dominated group, he gets ‘honorary’ status given to him. Women will hang on his every word more than he deserves, be deferent, overly-appreciative, they’ll subtly change everything to accommodate him - and they won’t even realise they are doing it. Female socialisation. That’s without even factoring his male socialisation and probable male entitlement.
This is precisely it. He is fawned over and his word is taken as having more weight to it. Additionally he automatically assumes he is he expert in the room on every given craft (our group encompasses 3 main crafts but we touch upon probably 7 others). Even if he has done the craft or not before he will talk as if he knows more than everyone else in the room, and more irritatingly assume everyone is a beginner in need of his tuition. He will stop women who did one of the crafts as their professional paid jobs for 40+ years and ask them of they want him to show them how to do something they could probably do in their sleep. And that's a quiet fairly mild mannered man.
Our group will never be women's only because its been historically open to both and the main body it's aligned to is open to both sexes but having been a member when there have just been women and when there has been a mix there is a perceptible difference