Surely, by now, after all those Employment Tribunal judgments...somebody in HR....or somebody in Legal...or the barrister.... must have scratched their head and thought...."oh hang on, we don't have a leg to stand on".
The sooner we stop having this "bring your whole authentic self to work and just do the job you are paid to do" the better.
I thought gender identity was supposed to be an internal feeling or belief. How dare the dog owner presume to know what the poor dog might be feeling.