What about beliefs that are beyond awareness? We hardly have insight into all our beliefs. For instance -- research in consumer behavior shows that we have quite irrational beliefs about the properties of certain products or brands.
It's tougher than I originally thought. For example, subjective probability of negative events is higher for anxious people relative to non-anxious, so this is the type of irrationality you would want to discourage as it is actually harmful.
On the other hand, normal, sane people are irrationally optimistic, whereas depressed people are more rational (famous finding, reference now escapes me). So, is this kind of irrationality to be encouraged or smacked down?
That's a very good question. I immediately think of the "positive affirmations" craze, which swept the US with claims that reciting positive statements to yourself (usually when looking in the mirror) can actually benefit you and help you to achieve your mental goals. There's little doubt that having moderate optimism is more healthy than not having it, but then there is the problem of whether actually believing the unlikely (albeit optimistic) is critical to the success of the affirmation therapy. Arguably, if you say and think wonderful things about yourself, where you are going in life, the kind of person you are, but criticize them ruthlessly, you may be no better off than if you had never considered the affirmations in the first place.
Where does one draw the line? I think that this is a question that should be continually explored by cognitive scientists. I'm pretty optimistic about the results :)