It may seem politically incorrect to call a mental health facility a nuthouse. But as far as I have been able to tell, it doesn’t offend the nuts (the patients in institutions) or their lay keepers (nurses, security therapy aides, activity therapists) who deal with each other hour-by-hour every day on a full work schedule. This crowd has a jaded sense of humor and few pc considerations (except perhaps about race) among themselves. They recognize various political risks and opportunities which an epithet offers at any particular moment, but they are not personally offended by “nuthouse”.
This category of “lay keepers” excludes doctors (psychiatrists and psychologists). They feel their special indignation over an insult to their much-maligned professional specialty, but probably not because anyone they know is called a nut.
Dictionaries almost always label the term “nuthouse” as offensive slang, but rarely assign that designation to “nut” when it means a crazy person. This enables the inference that any offense is to institutional, not personal, dignity.
Where polite society is valued by the bulk of its participants, it is created and maintained with live communication and continuing attention by individuals to each other’s sensibilities, not with a standard code specifying good and bad words for all. Where manners become broadly standardized in great detail, crowd control and politics are the real point, not interpersonal relations.
So we can dispense with any problem in using the word nuthouse. It just doesn't offend or emotionally damage the real people directly involved in nuthouses.
If our attitude, which is reflected by our choice of words, offends “the neighbors” or members of general society, that's a different issue. We have a right to ask why they care, when in all likelihood they have little or no contact with the people, nor any participation in the day-to-day environment, of state institutions which confine psychotic killers and perverts.
People want security. They don’t have a clear picture of what threatens their lives and happiness. Certainly the crazy and violent Other does threaten them, and so does their own immanent Mistake. Fear of the Other and fear of Mistake become the nuthouse. Your gut says it must be there, your mind hates to look.