Two conspiracy theories that I accept:

1. Vincent Foster was murdered.

2. The Church did not reveal the entirety of the third secret of Fatima. See also the book by Antonio Socci.

Elliot Sober begins his article Coincidences and How to Think about Them:

The naïve see causal connections everywhere. Consider the fact that Evelyn Marie Adams won the New Jersey lottery twice. The naïve find it irresistible to think that this cannot be a coincidence. Maybe the lottery was rigged or some uncanny higher power placed its hand upon her brow. Sophisticates respond with an indulgent smile and ask the naïve to view Adams’ double win within a larger perspective. Given all the lotteries there have been, it isn’t at all surprising that someone would win one of them twice. No need to invent conspiracy theories or invoke the paranormal – the double win was a mere coincidence.

Throughout the article, he recognizes that the “sophisticate” has a problem justifying his account by probability theory, at least in the sense that by any reasonable analysis, the naive account remains fairly probable. Nonetheless he betrays a strong desire to find a way to justify the position of the sophisticates, as for example when he says:

As noted before, it may be possible to provide an objective Bayesian treatment of Adams’ double win. Even though the FIX hypothesis has a higher likelihood than the FAIR hypothesis, perhaps there is a way to justify an assignment of prior probabilities that has the consequence that the FAIR hypothesis has the higher posterior probability.

This of course implies that a treatment that suggests that the lotteries were likely fixed is automatically not objective.

It may be easy to argue that many conspiracy theories are more a result of flawed mental tendencies than of rational thinking. But insofar as virtue consists in a mean, it is necessary to avoid the opposite error as well.