Theism is often a default test of irrationality on Less Wrong, but I propose that global warming denial would make a much better candidate.
Theism is a symptom of excess compartmentalisation, of not realising that absence of evidence is evidence of absence, of belief in belief, of privileging the hypothesis, and similar failings. But these are not intrinsically huge problems. Indeed, someone with a mild case of theism can have the same anticipations as someone without, and update their evidence in the same way. If they have moved their belief beyond refutation, in theory it thus fails to constrain their anticipations at all; and often this is the case in practice.
Contrast that with someone who denies the existence of anthropogenic global warming (AGW). This has all the signs of hypothesis privileging, but also reeks of fake justification, motivated skepticism, massive overconfidence (if they are truly ignorant of the facts of the debate), and simply the raising of politics above rationality. If I knew someone was a global warming skeptic, then I would expect them to be wrong in their beliefs and their anticipations, and to refuse to update when evidence worked against them. I would expect their judgement to be much more impaired than a theist's.
Of course, reverse stupidity isn't intelligence: simply because one accepts AGW, doesn't make one more rational. I work in England, in a university environment, so my acceptance of AGW is the default position and not a sign of rationality. But if someone is in a milieu that discouraged belief in AGW (one stereotype being heavily Republican areas of the US) and has risen above this, then kudos to them: their acceptance of AGW is indeed a sign of rationality.
People don't start out with a high/low claimed prior on lying climatologists and then decide to start arguing about global warming on the internet - it's vice versa, in most cases. The end result tells you about this whole causal history, which includes a fair bit of irrationality along the way.
Of course, where the causal chain terminates is often in stuff like "my parents had political view X," which we don't particularly want to learn about, and thus has to be controlled for if we want to learn about the intermediate irrationality.