This may end up going back to the courts. Lord Sumption among others has indicated that women + TW groupings are legal.
The logic for this is that trans discrimination protection only operates one way, ie it is legal to discriminate against a man for not being trans. So if a non-trans male wanted to attend a women + TW group, that group could say, we are discriminating against non-trans men not because they are male but because they are not trans, which we are allowed to do.
The question is whether the SSE can operate in this way, allowing non-trans men and non-trans women to be treated differently while also allowing transwomen to participate, and the EHRC may already be commissioning expensive legal advice on this.
However it may be a while, if ever, before this issue actually comes to court, as the optics are complicated and arguing it will involve arguing that men should have access to a womxn group, which as PP have pointed out most people will find uncomfortable.
Interestingly I can’t see any grounds for excluding transmen from a group of women. This is as it should be I think, and the transmen I know have always wanted more of a dual nationality approach to identity rather than a simple TMAM.
Speaking as a lesbian I don’t particularly like having TM in my spaces. I don’t like being around the testosterone, I find their regressive gender ideology often translates into overt sexist behaviour, plus their ideology is disrespectful to the non-trans masculine women who are the bedrock of our community. But if they are attracted to women, they are still part of the family. When they want to be with the rest of us I welcome them like any other family member you disagree with but would nonetheless fight to protect.