If an employer provided only male and female toilets/changing rooms and, for the purposes of this argument, provided accessible facilities for those with disabilities or access needs within such single sex facilities, then I think they're is a significant issue for some women who identify as men.
Such a woman may have had a double mastectomy, taken testosterone, have male pattern baldness, facial hair and "pass" as a man e.g. Stephen Whittle or Buck Angel for two examples, one who says he is a man, the other who acknowledges he's female.
The FWS judgment was clear that such women must not use the men's facilities because they are women and men are entitled to single sex facilities. But it is arguable (again as per FWS) that their presence in the women's facilities could be considered intimidating. Such women would need a third facility to comply with the law. If one wasn't provided, they would have a case of discrimination against their employer.
And if they did use the women's, that might out them as trans. So much as I know some people want accessible facilities to be in single sex facilities with cubicles for safety reasons, having an accessible toilet with a sink inside is the safest for their situation.
Many assume these are just for people with disabilities but many disabilities are not visible - someone with a stoma for example, or autism where they have a sensory issue around noise or smell.
Some people use them because they want privacy for a poo or menstrual issue.
So I feel very strongly that a third accessible facility is required so that trans men don't out themselves and comply with the law.