I'm not sure that the customer would have had a clue that the barista was trans-identifying, @EveryWitchWaybutLoose (great username btw). The only clue is his long hair, which is back in a ponytail, so may not have been visible to her and - even if it were - obviously plenty of non-trans identifying men have long hair.
She looks to be a similar age to me and, if she is anything like most people our age, she would not have been able to read his name badge without reading glasses on.
So, from her point of view, she refers to a man who is presenting as a man, as a man, then gets abuse screamed at her. She did really well to hold her ground.