I have an immediate family member who is bipolar and I believe his illness does influence his religious beliefs.
He has had visions of demons, he quits eating pork when in a certain mood, and he believes he is the religious leader of our family and knows what is best for us when he is sick.
I don't know about Mel Gibson but many creative people have suffered from bipolar and depression.
Edgar Allen Poe and Charles Dickens among them.
Before my relative was diagnosed bipolar he was a rising star in his career field and he was always very intelligent and athletic.
My prayers for your relative. I think he can still excel with proper treatment, but it is shame to see how destructive this illness can be not only to the one suffering from it, but to his family as well. You're right that they often have visions of demons, think they have a special calling from God, etc. They often see horrible things. It is a shame people can't understand that, occasionally, they have no control over what they see, think or say.