Trans women wishing to be treated exactly like other women will meet the same caricatures as other women do - the panomime dame, the dumb blonde, the gorgon mother-in-law, the mutton-dressed-as-lamb. All have a bit of truth to them, as well as a lot of exaggeration for dramatic effect. Anyone objecting strongly to one of them looks a bit of a po-faced killjoy.
I don't know how the drag students were played (and if it was rag week, the acting, costume and makeup abilities of the participants would be rudimentary), but if the trans women recognised themselves, it could be that was because the act had picked up on something that the trans women could see in their own mirrors, exaggerated like those standard comic characters.