Harold and Maude is my favorite movie, too, but I have a very different perception of it. I don't see Harold as mentally ill, for one thing. He's an angst-filled teenager (or young adult). He's bright, and rather lost; he feels unloved. He is being raised by a mother who cares more for show than substance and whose life is centered around her social engagements. She sees Harold as another accessory in her life, one that doesn't quite fit. (When Harold's mother decides it is time for him to marry, she fills out the dating service questionnaire with her own answers, not his.)
Harold goes to funerals; he craves the raw emotion and realness that accompany such occasions. Maude goes to funerals; she likes the pageantry of life. Maude blows Harold's mind. This is a coming of age story; she makes him uncomfortable, she leads him to question his life and his sense of morality (and mortality), his sense of what matters. She teaches him to play the banjo.
The priest and the therapist are stiff caricatures of society's mores. Maude stands out in bright contrast as a vibrant symbol of individuality. I see Maude as freeing Harold from his mother, from his confusion and neediness. She hands him the key to escape his old life and become his own person.