> conjunction fallacy [...] you pick ii, even though we know it's less likely
We know that "mental illness and odd beliefs" is less likely than "odd beliefs". That doesn't mean we know that "mental illness and odd beliefs" is less likely than "no mental illness and odd beliefs", which is the relevant comparison here.
(But, for what it's worth, I think most people who embrace conspiracy theories don't do so as a result of anything that would be diagnosed as a mental illness.)
We know that "mental illness and odd beliefs" is less likely than "odd beliefs". That doesn't mean we know that "mental illness and odd beliefs" is less likely than "no mental illness and odd beliefs", which is the relevant comparison here.
(But, for what it's worth, I think most people who embrace conspiracy theories don't do so as a result of anything that would be diagnosed as a mental illness.)