The classic case of a “symbolic belief” is what Orwell dubbed “doublethink”: propositions you profess publicly, maybe even sincerely believe you believe, even while, on another level, there’s some part of you that knows better, so that the false belief doesn’t actually get you into practical trouble.
Pseudobeliefs may serve any number of functions; I’m using the phrase “symbolic belief” for the ones that either work as a public expression of some associated attitude, or play some role in defining the holder’s self-conception. In a post from last week, a commenter pointed out that there really are vegetarians and vegans, especially in certain punk scenes, who purport to believe that animals are not only morally equal to, but perhaps even morally superior to human beings. As he also pointed out, though, none of them really act as though they believe anything of the sort.
I'm not sure whether this is something to rejoice about, but I think it's true. Most of the people who claim to believe that President Obama is not truly an American citizen seem to be suffering from a severe case of "double think." They certainly don't act as if they genuinely believe that a Manchurian candidate is running the country.
The same is probably true of the 9/11 Truth Movement. If the "truthers" sincerely believed that President Bush had murdered 3,000 Americans in order boost some Iraqi oil, they would've probably done more than parade around Time Square with picket signs and megaphones.