As Foodfiend says: inquire for the source of their information and then check whether this source was qualified in all the protected groups, their needs and rights, or merely just one of them?
And then mention that 'fair access' applies to nine characteristics, not just one. And that the EqA2010 requires proactive anticipation of barriers and needs, not reaction after discrimination (direct or indirect) is experienced. And then mention impact equality assessments as good practice (and this applies to all users of female toilets not just TQ+ people who wish to use them).
And then mention the obvious and anticipatable needs of:
disabled women
neurodiverse women
women of cultures and faiths such as orthodox Jewish, Muslim, Gypsy Roma Traveller
women who have experienced CSA, VAWG, trauma, DV, DA
women with menstrual and other biologically based challenges they may not be willing to deal with in a mixed sex space
And that obviously female people cannot be 'outed' or made to disclose highly sensitive information in order to be permitted a facility that they find accessible. And the percentage of female employees affected can be estimated against the percentage of TQ male employees wishing to use opposite sex facilities. And if some female employees end up needing to go off site to be able to access facilities have they checked how that might go in a court case about equality, and are they permitting the time for female employees to go and do this? And have they considered that this is likely to be sex based discrimination by law, because there is no equal impact upon male employees in this way, so female members of staff are being treated less favourably on the basis of their sex? (And quite possibly their disability/culture/faith/belief at the same time)?
So the obvious thing to do is provide proportionate accessible mixed sex spaces, and female only spaces, and to expect that all employees recognise that everyone's access and individual needs and diversity is equally important. And that not every single facility will be accessible or for the use of everyone.