50% of Americans think there was a wider conspiracy behind the assassination of JFK.
About 35% of Americans think that global warming is a hoax.
What you're doing is probably the conjunction fallacy. You see people with odd beliefs. You then have a choice: i) these people have odd beliefs ii) these people have a mental illness and odd beliefs. Even though i is more probable you have to explain the irrationality of the beliefs so yu pick ii, even though we know it's less likely.
Mental illness is very common (1 in 4 at any point in our lifetime; 1 in 6 right now) but these numbers talk about the widest interpretation of mental illhealth. Delusional thinking is thought to be less common. Mood disorders are thought to affect about 5% of the US population; schizophrenia about 1%. So you've suddenly diagnosed very many more people with a mental illness.