While it It may also be discriminatory to only have mixed sex provision, from the point of view of the service provider, the more immediate problem is that provision that includes people of both sexes is not single sex and must be managed accordingly. Unisex toilet provision is obviously legal, but the relevant building standards must be met.
Even if you do have a single-sex space, the exclusion must be proportionate, which means that the rights of whoever wants to be in a single-sex space, if they’re complaining, have to be counterbalanced against the rights of a trans person.
The proportionate test is whether the space can exclude people of the opposite sex, not whether it can exclude people who have a particular belief about gender.
For a service to be single sex, it must meet the criteria in the Equality Act. If some people of the opposite sex are included, then in most cases you will be demonstrating that the criteria have not been met so the service shouldn't be single sex.
(Children under 8 would be the obvious example of an exception, but this is a blanket rule for an objectively quantifiable group and at the discretion of the service provider.)
if they’re complaining, have to be counterbalanced against the rights of a trans person.
They might be able to argue that there aren't sufficient unisex/mixed sex provision, but there is no right to use services for the opposite sex. Similarly I can't argue that I have suffered discrimination because of my sex if I can't use a blue badge parking space.
Maybe if it was your personal liability on the line you might understand the legal quagmire they have been forced into.
FWS won the case that clarified the law for most trans people in 2022. If there had been more focus on practical solutions and less on arguing that sex is irrelevant, then service providers would certainly be in a better position now.