I don't find it offensive, just cringy and sometimes even humorous. I'm going to be completely open and honest here and expose myself, there was a time in my life where I struggled hard with mental illness. I was clinically diagnosed with psychosis. I had auditory and visual hallucinations, paranoia, anorexia, a whole host of issues. I was so bad infact I would have to turn the TV on when I was alone to drown out the screams I thought I was hearing. I was almost checked into a mental hospital, it was very bad. I wanted to kill myself to escape it. (And yes, sometimes I did unintentionally make crazy faces. Mostly frightened deer-in-headlights faces. Not those weird maniacal smiley fits of laughter that they're always portrayed as having??)
Obviously, years later, I am a functional adult human being who does not suffer with it anymore, at least to that extent. I went through lots of therapy, had tried just about every medication under the sun. Maybe it was the emotional support animals, maybe it was my human support team, maybe it was my shift in (or out of?) religion, maybe it was the cannabinoids. Who knows. Either way, I'm better now. And because of the whole ordeal I'm able to grasp media portrayal of insanity with a whole new understanding.
I like mentally ill characters when they're done well because it introduces average viewers to a very real thing that people suffer with. Not just insanity, but depression, anxiety, PTSD, etc. I think shows like Netflix's Bojack Horseman do a remarkable job of covering such topics. But I also sometimes just like crazy characters that are crazy just to be crazy. Sometimes they're really funny. No harm done.
I will say this though, I feel as if what I have endured has made me a much better writer of mentally ill characters. Alise, my antagonist(?), has psychosis and PTSD, two things I have dealt with. She is mad. Absolutely batsh​t crazy, but I love writing and drawing her. She's such an emotional being. I feel like she is an outlet for me to work out my own traumas in these areas, albeit to an extreme. Alise is a murderer, while I am not lol!
Edit: DeviantART style crazy creepypasta fanart is really weird and inaccurate and fetishizes insanity in uncomfortable ways and I'd rather take bad sonic fanart over it tbh lmao