I don't think it's insulting or ridiculous to have that conversation at all. One of my favorite literary discussions is in fact the mental state of Sherlock Holmes and whether or not he had a mental disorder and how that contributes to the understanding of the stories Doyle wrote. It's actually a fascinating discussion given that mental illnesses weren't clearly diagnosed at the time the way they are today, so Doyle must have been writing on his own experiences with patients or possibly a friend.
There is much to be gained from the discussion, since talking about a character's mental state could easily give rise to an idea of their motivation. If you don't think a musical character deserves to be read into that much, you demean the art form. It's a common topic when talking about classic plays including Ibsen, Miller and of course Shakespeare. Why not musicals too? Not to mention it's a bit fun.
So, I'm not going to deprive myself of that. Throwing a few beyond just bipolar out there:
Mrs. Lovett- BPD (if you believe in that disorder)
Sweeney- sociopath
Sally Bowles- BPD
Stine (City of Angels) - schizophrenia!
Oscar (Sweet Charity)- Panic disorder
Nathan Detroit- Pathological gambling
Caroline (Caroline, or Change)- depression (?)
Frederik (A Little Night Music)- Schitzoid personality disorder
Cora Hoover Hooper (Anyone Can Whistle)- Narcissistic Personality Disorder
And of course, the various assassins in 'Assassins' each have their own string of crazy based on their respective historical figures.
I don't see the harm in the exercise, I don't see how it's insulting either. I know from the Sherlock Holmes discussion that many people I've spoken with about it frequently like to 'claim' Sherlock as their own disorder- it's quite funny to watch how frequently it happens actually.
"Are you sorry for civilization? I am sorry for it too." ~Coast of Utopia: Shipwreck