I read all the posts on the toilets conversation thread that was deleted, up to about page 18.
I kept looking for an opportune moment to comment but it never came.
I was very disappointed with the thread right from the start because I felt that there was an unnecessary conflation of single sex toilet facilities (a valid and important discussion) and a fear/mocking of a transwoman who "giggles, flicks hair" etc. The two are very different subjects.
Any transwoman can wear any clothes and behave in any (legal) way they like. If that male does so in a caricature of "womanhood" and then gets a contract promoting sports bras, calling attention to the disgust and outrage at their misogyny seems fair game. If that transwoman is attending a workplace to do their job, I would agree that any calling out of their dress/mannerisms is unnecessary and transphobic. At least one poster did try and call that out.
From the start, the comments were toxic and unhelpful in many cases, whether "GC" or "TRA" in style.
Regarding toilets, what I had intended to add was that I would very much add my voice to a call for third spaces. Sadly the prevalence of GAP (please rearrange) in transwomen is high. This also impacts transwomen with dysphoria (as many posters have pointed out) because it skews the view that people have of transwomen. However, as is with the case of all single sex spaces the risk of harm against women is what's being mitigated. It doesn't matter that many biological men or transwomen will have no intention of causing harm to women. The safeguard is there to stop the few that would.
For the sake of Lucy and the women's dignity, IMO the women's toilets should be for the women only. It is very likely that Lucy or any transwoman would not feel comfortable in the men's toilets, therefore a third space is appropriate. If any transwoman believes that this is not supporting all dignities, I would suggest that they need to examine their own reasons as to why it's so important that they use women's facilities. Dignity and safety for all is key here.
Personally, I am glad that the post got deleted. And no, I didn't report it.