With that throat-clearing done, the main issue is what Steve Bloom and Michael Mann said, in effect that the Powerful Groups Are Lying (PGAL) model better explains why the public has problems accepting climate science. Some organizations and people are lying and acting in bad faith, feeding into and creating the cultural identity that Kahan researches. My own suspicion that climate deniers are cozying up to evolution deniers is a conscious effort to snuff the Creation Care evangelical movement and preserve a conservative religious group identity, so this identity that Kahan talks about isn't a fixed thing - it's manipulated.
Secondary to all that, Mooney overplays it when he asks whether the Kahan paper will "slay the 'deficit model' once and for all." The study showed that highly numerate people were better than innumerate ones at understanding a problem, even when that understanding conflicted with their group identity. In the paper, Kahan says (p. 25):
ICT predicts that more numerate individuals will use that ability opportunistically in a manner geared to promoting their interest in forming and persisting in identity-protective beliefs.That seems to be either wrong or sloppy writing because the highly numerate people did better despite the group identity cost, presumably by using their better skills. The general argument in the paper is fine that polarization increases - both groups do better at high numeracy but one will do far better than the other when it reinforces their identity. If both improve then the deficit model isn't slain.
The results in the experiment suggest that high-Numeracy partisans did exactly that in the gun-ban conditions.
Mapping this directly to climate change, it suggests that both reasonably-educated conservatives and liberals will benefit from more science education on climate, although it will penetrate better with liberals. The real need, though, is for the PGAL effort to stop manipulating group identity and force-feeding disinformation.
Kahan's right though when he says "people, once predisposed, misinform themselves, summoning all their reason." That may be a common flaw, but it's still a moral flaw. The disinformers who feed this weakness are the crack dealers of politics.
I should also say not all the deniers know they're lying, and from my conversations with some of them I'm sure they believe what they're saying. Others though are a different story.