The hero or heroine's misbeliefs can change over the arc of the story or scene. If the author writes well enough, we root for this change or changes.
Not many of you know that I'm a U.S. chess master. I knew Bobby Fischer. We analyzed games together along with a group of his friends. Yes, he had friends, and always had time from his rigorous ascent to the World Championship to kibitz. He was witty but never veered far from the point, chess, our chess and how we could improve.
A young Bobby's mom was the subject of constant surveillance by J. Edgar Hoover's overly zealous FBI during the McCarthy and blacklist era. A young Bobby internalized this justified paranoia and with no father and desperately wanting to both love and run from his mom—his mind cracked under the strain, IMO.
The movie, Pawn Sacrifice, simplified the story and stayed on point. I want to present a lighter side of Bobby, the side I knew. I abhor his anti-Semitism but find his cold war instincts compelling. Bobby was Jewish but when you see his backstory and understand his need to be loved by someone Jewish (his mom) the U.S. government harassed (and perhaps rightly, I don't know) you may at least understand him a little better. If you see these signs of abandonment in a child try to find a way to help. All Bobby knew well was chess, even though his IQ was a 210. This genius made it easy for him to quickly jump to conclusions without missing any proofs along the way. Unfortunately, chess is a closed system and the world is not.
Here's the great Bob Hope versus Bobby Fischer, 1972:
Can you write a character like this? Would you want to?