None of this changes the fact that single-sex services are both permitted by law and preferred by users.
Any argument that, say, single-sex toilet provision is equivalent to Jim Crow laws would be laughed out of court. And who is going to sue the HSE?
Service providers who allow selective opposite-sex use of single-sex services are asking to be sued, both for direct and indirect sex-discrimination. High Court says the result will depend on the fact evidence. There have been at least two cases where providing only a mixed-sex (ie 'trans-inclusive') service was found to constitute indirect sex-discrimination against women (because they are more disadvantaged by it than men are).
The only reason to provide a 'trans-inclusive' service is ideological, not legal.
There are two arguments for trans-inclusive services.
One: it doesn't vitiate the single-sex nature of the service, cf small children, plumbers etc. Rejected by High Court.
Two: forcing trans people to use services for their own sex, or a unisex alternative, is outing, and therefore illegal discrimination as to gender reassignment. Also rejected by High Court.
Jurisprudence currently has 'trans rights' on the back foot.
Your move.