Note that holding contradictory beliefs is fairly common of conspiracy theorists (link):
Another study titled Dead and Alive: Beliefs in Contradictory Conspiracy Theories managed to show that, not only will cranks be attracted to and believe in numerous conspiracy theories all at once, but will continue to do so even if the theories in question are completely and utterly incompatible with one another. For instance, the study showed that: "... the more participants believed that Princess Diana faked her own death, the more they believed that she was murdered [and that]
Citation: Wood, Michael J., Karen M. Douglas, and Robbie M. Sutton. "Dead and alive beliefs in contradictory conspiracy theories." Social Psychological and Personality Science 3.6 (2012): 767-773.