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.
Presumably most of those whose opinions fall outside of whatever the acceptable range is have those opinions either because they believe they have some relevant piece of expertise, or because they believe they have some relevant information about the biases of specific experts, or because they don't believe that their ability to estimate systematic bias is in fact "very poor", or even because they disagree with you about what the experts think. This seems like the sort of information people might falsely convince themselves that they have, but at least if we're no longer just looking at relatively narrow and technical questions like attribution and sensitivity but also at broader questions like policy, where expert consensus becomes harder to characterize and many different fields become relevant (including futurism and rational aggregation of evidence and weighing of considerations, which many LessWrongers are probably better at than most domain experts) the possibility that they're right surely is not so preposterous that we can hold it up as a stronger rationality test than theism.
You're right of course - having policy niggles or disagreement is not a good sign of irrationality. But the harder the science gets, the more disagreement becomes irrational. And I've seen people cycle through "global warming isn't happening" to "it's happening but it's natural" to "it's man-made but it'll be too expensive to do anything about it" in the course of a single conversation, without seeming to realise the contradications (I've seen theists do the same, but this was worse).
So yes, mild anti-AGW (or anti-certain AGW policy ideas) is not a strong sign of irrationality, but I'd argue that neither is mild theism.