Oh yeah, the general public has no fucking clue what actual psychiatric disorders look like, and that includes the media

It's much more complex than that. Religious delusions are culturally bound. I've seen hyperreligiosity in Hindus, New Age Crystal practitioners, and even atheists. Atheists may have a supreme feeling of being one with the earth. All of this is often paired with increased goal directed activity, lack of sleep, and some truly bizarre plans.

I've personally never seen anyone burn or cut a religious symbol on themselves based in psychosis though. Self injury like that is more often a sign of borderline personality traits rather than an axis I psychiatric disorder.