What I was getting at in my last sentence was not questioning the exorcist's belief, but the actions of someone e.g. with no belief in demons at all who had a friend or family member who believed and wanted an exorcism.
So long as the exorcism wasn't physically harmful (like some non-RC versions are, people have died!) it might arguably be better for the person not to discourage them and not to lecture them about atheism or skepticism or whatever unless/until they're better, assuming there is a placebo effect on their mental state in a positive way?
But that's just an idle thought based on memory of something said in a movie.
You see, thing is, there are no demons. If someone believes they are possessed by demons, they do indeed have a problem, and one that needs to be addressed by scientific medicine, not some superstitious retrograde nonsense.