The Equality Act 2010 allows for single-sex stipulation to be made if it is a proportionate means of achieving a legitimate aim.
I'd say the aim of having a lesbians', or gay mens', dating night be for one sex only is legitimate and simply stating it to be so is a proportionate means of achieving that legitimate aim.
What was all that campaigning for gay rights about, and what do gay rights even mean, if anyone at all can claim to be the sex they wish to be?
Of course it does. And doing so could have been done within the law without needing to know about anyone who for any reason has chosen to attend the event.
However the organiser chose to use as her reason a graphic description of someone who may or may not have been a transperson. Understandably transactivists were annoyed about this and considered her comments as transphobic.
The stereotypes of Jewish people sometimes portrayed have been roundly condemned and are not acceptable. Why then is it OK to accuse someone who wore lycra and apparently had an erection (personally I think it was the old rolled up socks trick) of being a transwoman. They might have been or they might not.
She also discussed an incident in a toilet which was almost an assault.
Now both of these incidents could be true. The problem is that in seeking to make the event only for natal women the organiser used them as examples of transwomen's behaviour and reasons why the event shouldn't be open to transwomen. Transpeople naturally found that offensive.
As I have said she did it badly. It could have been done legally and without reference to any behaviour.
It isn't fair or just to accuse a whole section of society of bad behaviour because of one or two individuals