Interesting points LRD about how it would be virtually impossible to screen all entrants to the event to ensure they were entitled to attend. Interestingly enough, apart from some kind of medical test, the only way to assess would be reliance on (gasp) gender-based characteristics (the same ones most feminists and yes, most trans feminists reject!)
Widow, where you and I part company is that I do believe there are benefits in activities, meetings, etc. that are designated for specific groups that experience social, economic and political disadvantage in society. Men as a group don't. Women as a group do.
However, a group for disabled men (who experience disadvantage) would be legitimate in the way that a group for non-disabled men (who are more privileged because they are not disabled) would not be.
Similarly, an event for people of colour would be relevant because despite the diversity of ethnicities, cultural, faith, linguistic, etc. backgrounds, they will all in some way have been on the sharp end of racial discrimination or oppression in the UK in some form. An event for white people only would not be the same.
I also agree that within say a women-only event, it's legitimate to have specific meetings, groups, etc. for women who experience intersectional oppression due to misogyny and one or more other factors related to their identity. For example this could be Lesbians, older women, women of colour, disabled women, working class women, and trans women.
But, imho, it doesn't work other way around to have an event that is for women (because of their shared identity and experience of oppression as a group) that excludes a sub-group of women who experience intersectional discrimination. I accept that indirectly, there are events that are "women-only" that effectively exclude disabled women (e.g. held in inaccessible venues), women of some faith traditions (e.g. held on a Saturday,) or low income women (e.g. high fees, travel costs, etc.), but having an event that so explicitly excludes a group of women who experience intersectional oppression is what has been so jarring.
The nut of the issue seems to be that some feminists flatly refuse to countenance that trans women are women. No evidence, whether scientific, social, political or personal will shake them from this belief and it appears that no anecdote or thin theoretical risk is too outrageous to use in defence of that belief.
I had a great aunt who grew up with racial segregation in the American South and was horrified by the civil rights movement in the 1960's. She went her grave a few years later with the unshakable belief that African Americans were a kind of sub species and not fully human as white Americans were. I'm remembering my overhearing of her conversations with my polite-but-not-persuaded mum when I see tweets and blogs and discussions insisting that trans women can never, ever, under any circumstances be "genuine" women.