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.
I considered downvoting your post after reading steven0461's comment; his basic point is definitely worth keeping in mind. But I decided against it as I think your basic line of thinking was fair, and in fact I probably would've upvoted your post had you
elaborated on specifically which aspects of the AGW hypothesis you'd propose as rationality probes (e.g. whether human activity can raise CO₂ levels in the troposphere, whether tropospheric CO₂ levels have risen over the last x years, etc.)
made the weaker (and easier to defend) claim that AGW denial (with "AGW denial" having been fleshed out as suggested in the previous bullet point) was about as good an irrationality test as theism, rather than a better one
I expect the remaining objections to AGW-denial-as-rationality-test would apply just as much to theism-as-rationality-test, in which case it'd still be justified to say the former is as good as the latter. Theism correlates with partisan politics too, and if anything gives fewer bits of information about someone's rationality (being basically a yes-no condition) than AGW-denial-as-rationality-test (which could be a sliding scale). I'm not 100% sure that trying to probe rationality in this way is worth the effort, but again, this objection applies as much to theism as AGW denial.
[Edit to rephrase "even more binary" in terms of giving less information.]
Fair points.