If they don't they will be open to legal claims of indirect discrimination so it's in their interest to provide them. Yes, it's legal to have mixed sex toilets - sungle occupancy disabled toilets are in effect mixed sex. What you can't do is call a service single sex and then let the opposite sex use it, or in fact just certain ones of the opposite sex. It then becomes a mixed sex service, which in some circumstances might be considered discrimatory against women, eg ok if it was a shoe fitting area but not ok if it was a communal changing room.
If a restaurant is non smoking, you can't let just certain people smoke. It stops being non smoking altogether.
It's increasingly clear to me that you don't grasp the basic issues.
Nothing is a mix if contains only one thing. This is the extent to which the language has been switched to accommodate the gender critical ideology.
If a private toilet can be used by anybody, then it is a universal toilet, such is the case with facilities for disabled folk. A locked door establishes the boundary for privacy (not dignity which has a different legal meaning).
What you are calling for is single sex hand washing facilities because these tend to be communal - which does not mean ''mixed sex'' either, but multiple user.
The Scottish schools case is frankly ridiculous as it comes from a 5 year old girl (who I agree has rights) was objecting to the toilet arrangements because she doesn't like the noise. She says some boys are noisy. Isn't it true that some girls are noisy? What would you say to a five year old boy who doesn't like the boy's loo because it is too noisy?
So what will be next, women's facilities must have accoustic treatments?