I don't know much about these menopause support groups but I used to run a breastfeeding support group and the whole purpose of the support group was that it was peer to peer. I hosted the group, I could help solve common breastfeeding issues but a lot of the support actually came from service users to other service users to bring a community of people who were all going through the same thing, to share the highs and lows and collaborate on creative solutions when issues were not quite so straightforward.
I expect the same would go for a menopause support group in principal.
If a transwoman turned up to any of my groups they would be out on their arse faster than they could say nipple secretions. A lot of the women I supported were from minority ethnic backgrounds. Some women came from a culture of postnatal confinement and came out of desperation, some came from Muslim or Jewish backgrounds where exposing certain parts of their body whether that was hair or breasts to men that were not their husband or relatives was not allowed in their religions and my primary purpose in these groups was to facilitate comfort and safety whilst preserving dignity.
A breastfeeding support group is no place for a man. The men who wanted to support their wives were always welcome to make a private appointment or make a phone call to us or the national breastfeeding helpline. They could also consult Google or even a forum, like mumsnet, dadsnet or... gulp, reddit, but basically there is a plethora of information available to them in various other sources without invading a woman's group.
I wish NC had gotten the opportunity to ask why, if in good faith he would only seek to support his loved ones, he couldn't consult these other services - out of business hours like he kept bloody insisting gender critical women do.