John Quiggin ponders right-wing agnotology:

A recent report on a poll finding that a majority of Republicans (that is, likely primary voters) are “birthers”, with only 28 per cent confident that Obama was born in the United States has raised, not for the first time, the question “how can they think that?” and “do they really believe that?”.
Such questions are the domain of agnotology, the study of culturally-induced ignorance or doubt. Agnotology is not, primarily, the study of ignorance in the ordinary sense of the term. So, for example, someone who shares the beliefs of their community, unaware that those beliefs might be subject to challenge, might be ignorant as a result of their cultural situation, but they are not subject to culturally-induced ignorance in the agnotological sense.
But this kind of ignorance is not at issue in the case of birtherism. Even in communities where birtherism is universal (or at least where any dissent is kept quiet), it must be obvious that not everyone in the US thinks that the elected president was born outside the US and therefore ineligible for office.
Rather, birtherism is a shibboleth, that is, an affirmation that marks the speaker as a member of their community or tribe.

I do agree with Quiggin that some conservatives who espouse the belief that Obama is a Muslim or a non-citizen don't quite literally believe this. They believe it and don't believe it at the same time -- they believe it is the kind of thing Obama would do, whether or not he's actually done it. Quiggin argues that some form of this belief/non-belief can be found in partisans of both parties, and I agree.

But I do think the concept of agnotology applies here. Quiggin's argument hinges on the fact that conservatives understand that some people do not believe President Obama was born outside the United States (or is a Muslim, or...) But what those conservatives believe is that they enjoy access to truth that is denied Americans who are brainwashed by the mainstream media. The believe that Fox News is not just a network that counteracts the biased liberal media, or even a network that reports the stories that the liberal media ignore, but the vehicle for Truth:

You can find beliefs like this on the Howard Zinn/Noam Chomsky left, but not in the mainstream liberal left. You don't see Rachel Maddow claiming that the mainstream media is full of lies, and that she can deliver her viewers the Truth that is being systematically covered up elsewhere. There's no Maddow University

This kind of belief system, a claim to totalistic Truth that is denied outsiders, is common among cults and other subcultures. The new development is that it has become a significant, and possibly the majority, belief among a major political party. Now, obviously, there is some difference between believing that everybody knows a certain thing and believing that you and your fellow adherents know something that other Americans do not know because of brainwashing. But it seems like a distinction without a difference. And so this circles back to the epistemic closure issue, and the powerful effects of a closed information system in which misinformation can circulate unchallenged endlessly.