In Israel, a guy came in uniform with his gun for lunch (IDF guys always have their guns with them). The Hotel asked him to take it out of sight and change his clothes....
Do surgeons go around in their overalls? lifeguards in their swimsuits? both save lives.... (for a minute, picture Pamela Anderson walking around in a hospital.)
I live near Aldershot, the military doctors do not wear uniforms and the soldiers do not wear uniform at the hospital; Frimley Park and Aldershot is shared with civilians. But injured soldiers in Frimley Park A&E, of course come in uniform and there is no problem. Sandhurst military personnel is not allowed in pubs/restaurants in uniform.
Saying that, this guy, Mark Prendeville, was injured at the training field, he had to be there in uniform, as the priority was to treat his burns and definitely not to change his clothes! The hospital staff was out of order, his burns was the priority.
It's a matter of etiquette/protocol, nothing to do with military haters!