I’d be a bit more direct and simple.
“I’m writing with regard to this incident at your hotel on (date) which has been the subject of a thread on Twitter (link).
I would like to express my support for the employee who directed X to the unisex changing room. Since X is a self-admitted male, this was entirely appropriate and lawful.
Ensuring that single-sex spaces for women are kept that way is important for safeguarding reasons as well as protecting the privacy and dignity of women and girls. Please ensure that the employee in question is thanked for her work in upholding the law and the rights of women and girls.”
I wouldn’t bother with all the “I’m not anti-trans but…” or suggest that disciplining or retraining the employee is even a possibility.