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.]