Don't neutralize culture
Kahan is the head of the Cultural Cognition Project, a research group dedicated to investigating Grid-Group Cultural Theory. Or rather, investigating one particular interpretation of GGCT. The CCP version of GGCT differs in several ways from the original version of GGCT as formulated by Mary Douglas and Aaron Wildavsky. Of relevance here are the ways the CCP 1) psychologizes culture, and 2) treats culture as bias.
The CCP psychologizes culture by treating cultural worldviews as personality types. I'm not sure if Kahan would explicitly endorse this view, but in practice his research works on the assumption that people just are communitarians or hierarchists, etc. This then leads into the issue of treating culture as bias. If people simply are of one cultural orientation or another, then the only way we can get anywhere is to try to neutralize culture. Culture distorts our thinking, and we're better able to reach agreement and see the science clearly if we can get culture out of the way. Kahan is very explicit on this point -- his goal is to find ways to reduce the relevance of cultural cues in political decision-making.
Roberts' response pushes back at these two points. Roberts says -- and I agree -- that culture matters. It's important whether we structure our society in a communitarian or an individualist way. There's no shame in desiring (say) a communitarian society. We can't simply set aside culture as a bias so that we can make decisions like bloodless technocrats. If views on climate change are driven by culture, then what we need is not a way to neutralize culture, but a way to inspire people to understand the merits of our preferred way of life. Douglas and Wildavsky saw this quite clearly -- Douglas wrote an article called "Being fair to hierarchists" in which she extolled the virtues of her (heavily Catholic) hierarchical orientation, while Wildavsky was a noted libertarian (individualist) thinker. Both of them also recognized the importance to society of input from all cultural orientations. But this is quite different from the CCP quest to neutralize culture. With respect to climate change, culture can't be neutralized without eviscerating the very things that make climate change worth caring about in the first place.