This is how Conspiracy Theories are born:
All conspiracy theories are based on an initial hunch sparked by a pattern of clues, facts and events. This pattern is (mostly) based on sound reason and therefore will be considered by the perceiver to be true. The more clues/facts/events that add up thereafter, strengthen the perceiver's belief of his/her..."story" to the point where they present it to others; and the more people are involved the more complexity it gains and the more information(a.k.a. arguments to prove its credibility) it "contracts".
The driving force for the creation of a conspiracy theory is the feeling that something sinister is going on in the world something we cannot "see" or control (paranoia). This is what causes the "hunch" to occur and the rest is a landslide waiting to happen.
You see, the brain operates this way; it is a pattern seeking machine that will observe, gather pieces of information and connect them in a way so that a meaning can be abstracted, tested, expressed and then use the feedback to reach a conclusion. A psychotic/paranoid individual would, in a way, reach a conclusion first and then do the rest.
This is how/why people come to believe in Conspiracy Theories:
Whether a theory is true or false is almost impossible to tell because you can't possibly know all the facts or events surrounding it therefore you cannot reach a safe conclusion. It is your "instinct" and the sum of your experiences that topple you to one side or the other. The fact that someone might believe in a conspiracy theory simply tells you that this individual has received enough information (filtered by his/her overall experiences and his/her critical ability) to back it up and less or none to debunk it.
The answer:
Whether the individual is irrational/psychotic/paranoid is simply another contributing factor to the equation possibly hindering or biasing his/her critical ability hence rendering him/her more susceptible to believing in theories and has (almost) nothing to do with the theories themselves. (So it can definitely not be used as a general rule to describe "people believing in conspiracy theories").