I hope this thread and it's two purposes make sense. I want to talk about language first.
Unisex - One google result was "Unisex is an adjective indicating something is not sex-specific, i.e. is suitable for any type of sex. The term can also mean gender-blindness or gender neutrality. The term 'unisex' was coined in the 1960s and was used fairly informally. The combining prefix uni- is from Latin unus, meaning one or single."
When I see the "uni-" prefix I think of something that is suitable for both sexes, but is only for one sex or the other at a time - for example a single occupancy toilet with sink accessed directly from a corridor. Is this how most people use the term? I think it should be because we have other words to describe other types of facilities.
Gender neutral is nothing more than a term for mixed-sex, in my view, and we all know what mixed-sex means. There is no such thing as a mixed-sex theatre or restaurant - mixed-sex means a space which many/most people would expect to be single-sex but isn't - it is a multi-occupancy space with both sexes. I presume some use "gender neutral" to refer to single occupancy spaces that allow in both sexes, but I think it is helpful to keep unisex for single occupancy, and never use the term gender neutral at all (not least because sex and gender are different and we divide spaces by sex not gender, and always have.)
I think that for many many people single sex is best, not least because (dependent on exactly what the facility is) you are safe behind two doors, not separated from the corridor by a metre and two inches of wood, and when you leave the single occupancy cubicle you have a second safe space with potential help / support from other members of your sex.
For other people a single sex, single occupancy unit directly off of a corridor might be preferred as the best option for them. Some of these people might accept a unisex single-occupancy unit as better than a single-sex multi-occupancy space.
For reasons of practicality and cost it has to be the case that single-sex multi-occupancy has to be the default. And that they work for most people.
I genuinely believe mixed-sex spaces should be resisted at all costs because they endanger women. Campaigning for mixed-sex spaces is like campaigning to remove the fencing from a cliff-top path because some people prefer a less obstructed sea-view. It is morally wrong. It puts people in danger. Just because some people want something it doesn't make it right.
Disabled facilities are clearly required for the disabled. Non-disabled people should be discouraged from using them, obviously.
Where this becomes really interesting, in my view, is this. If we assume that we're going to go to the cost and trouble of accommodating a section of society who refuse to uses correct-sex, single-sex spaces, or who "can't" according to their claim, then what about me? I could quite easily choose to refuse to use correct-sex single-sex spaces. I can claim - with a large amount of honesty - that when using toilet facilities or getting changed I would prefer a special single occupancy space just for people like me, as opposed to having to share with others. What is it about trans people that means they have any greater claim to special treatment than I do? In my view they don't. In my view special treatment should be for people who need it (e disabled facilities), or for when society deems it good for society (not the sub-group) that special treatment is given. In this context I might argue that unisex facilities might be provided for bearded TIFs who might pass (because their presence in a single sex space for women could cause problems due to the perception being different from the reality). In contrast there is no need for special facilities for TIMs.