The big issue is that single sex facilities are required by all sorts of regulations, from building to workplace to health and safety regs.
Gender neutral toilets MAY be provided in addition to single sex toilets, and are acceptable as replacements if there is insufficient space for single sex facilities.
The specific big issue with the case quoted in the OP is that the council appear to have re-badged the existing women's and men's toilets as 'gender neutral'.
This is not allowed: there is a specification for a 'universal' gender-neutral toilet, and it has to be an enclosed cubicle which contains handwashing facilities as well as a WC. Existing single-sex toilets are not like this, and so can't be considered 'universal' gender neutral toilets, just because somebody has stuck a different badge on the door.
You suggest it's no big deal, just make all toilets in public buildings gender neutral. But this would involve installing building-regs-compliant 'universal' toilets, not just re-badging existing single-sex toilets, in all public buildings, and the cost in terms of disruption and expense would be huge.
It seems unreasonable to commit such a large amount of public money to changing an existing configuration - women's, men's and disabled toilets - which works for the vast majority of the public, to facilitate such a tiny percentage of the population.