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Eliezer_Yudkowsky comments on Reversed Stupidity Is Not Intelligence - Less Wrong
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If the same majority of smart people as stupid people are conservative then the statement that "Not all conservatives are stupid, but most stupid people are conservatives." is actually completely irrelevant, but I don't think that anyone believes otherwise. If there is a positive correlation between intelligence and the truth of one's beliefs (a claim the truth of which is probably assumed by most people to be true for any definition of intelligence they care about) then the average intelligence of people who hold a given belief is entangled with the truth of that belief and can be used as Bayesian evidence. Evidence is not proof of course, and this heuristic will not be perfectly reliable.
Why would the number of stupid people who believe something anticorrelate with the number of smart people who believe it? Most stupid people and most smart people believe the sky is blue. A shift in the fraction of stupid people who do X can take place without any corresponding shift in the fraction of smart people who do X one way or another. Some smart people actively prefer not to affiliate themselves with stupid people and will try to believe something different, but they are committing the error of the OP and should not be listened to anyway.