Logic detected: nil.
The changing room was for WOMEN, not for NON-MEN. (If you want the closest NON-MEN changing rooms, go to Scotland and search up Patrick Harvie's sleeve, probably). But if the only choices for changing rooms are "women" and "men" - which are the only sexes for which provision is legally required in the UK - where do you suppose a male nonbinary person should most reasonably and equitably go?
Plus the sheer regressive right-ring 1950s-ness of assuming one must use the women's changing rooms because one is trying on "gowns". 