We conducted a one-year longitudinal study in which 600 American adults regularly reported their climate change beliefs, pro-environmental behavior, and other climate-change related measures. Using latent class analyses, we uncovered three clusters of Americans with distinct climate belief trajectories: (1) the “Skeptical,” who believed least in climate change; (2) the “Cautiously Worried,” who had moderate beliefs in climate change; and (3) the “Highly Concerned,” who had the strongest beliefs and concern about climate change. Cluster membership predicted different consequences: the “Highly Concerned” were most supportive of government climate policies,but least likely to report individual-level actions,whereas the “Skeptical” opposed policy solutions but were most likely to report engaging in individual-level pro-environmental behaviors. Implications for theory and practice are discussed.(my bold). This has eerie echoes of Climate chickenhawks (which I re-found via my The Climate Change Hypocrisy Of Jet-Setting Academics?).
They say "Of primary interest was the level of belief in climate change—regardless of cause—over time". This is a problem, as the study runs for only one year. So I'm doubtful that's interesting; more promising is "we found that participants subdivided into three clusters as a function of these belief trajectories". There's a pile of stats there, which obviously I didn't bother wade though, instead I just read their conclusion: Despite these findings about climate change beliefs, self-reported behaviors, and policy support, we were unable to explain why the “Skeptical” low-believers were more likely to self-report more pro-environmental behavior than high-believers. They then go through a list of all the obvious excuses. The one I'd favour - assuming we're far too polite to go for "people are a bunch of hypocrites" - is that "the concerned" are in favour of unified political action, as indeed was discussed in Climate chickenhawks, whereas "the skeptical" as rugged individualists disposed to individual action.
At this point we need to look at the "action" options: public transport, re-usable shopping bags, eco-friendly products. And we observe that all of these would make perfect sense even without a GW problem. So you can perfectly rationally support them, even if you don't "believe in" GW.
Another point that needs clarifying is quite what "believe in" GW might mean. I am perfectly capable of sustaining a clear distinction between believing the science, and the policy options. But long years in the blogosphere convinces me that most people are not. So for most people it is hard to tell whether they really disbelieve the science, or dislike what solutions they think you're going to propose (Rejecting Climate Change: Not Science Denial, but Regulation Phobia?).
TF offers the conclusion: If the effect sizes are material, the implication is obvious. Improve the environment, support skeptics. I doubt that works; the skeptics are there already. How about the opposite: convince "the concerned" that individual action is also worthwhile? All that individual action only gets you so far (though as I said in Cl Chk, more individual action will act as useful signalling), so some kind of collective action is likely necessary. Again as per Reg Phobia, the key to that is the type of solutions you're proposing. As Hayek says, it is possible even for a Hayekian who doesn't believe in central planning to rationally desire some taxation (WMC interpolation: e.g. carbon taxes) if they accept there's a problem.
It's all about vested interests
Related, but not the same, Graham Readfearn, in the Graun points to Relationships among conspiratorial beliefs, conservatism and climate scepticism across nations (Matthew J. Hornsey, Emily A. Harris & Kelly S. Fielding, Nature Climate Change (2018), doi:10.1038/s41558-018-0157-2.) though I wasn't terribly interested in that, more in the Attitude Roots and Jiu Jitsu Persuasion: Understanding and Overcoming the Motivated Rejection of Science. Though it has too much sociology for me, it is perhaps a useful list of proposed explanations for behaviour.
* Eating their own, eating their own… by Timmy. concerning (hush yo mouth!) l'affair Schneiderman.