The first paragraph of the letter (after the abstract) almost perfectly identifies the problem, although the authors, being social "scientists", predictably fail to understand the implication: "As members of the public do not know what scientists know, or think the way scientists think, they predictably fail to take climate change as seriously as scientists believe they should."
The same is true of climate change, diet, exercise, privacy, foreign policy, gas mileage, law, and so forth: The general public does not take any of these issues as seriously as specialists in those fields think they should. This is not because the specialists are right, though; it is because the specialists devote their careers to those areas, and as a result have a distorted view of how much concern the average citizen should dedicate to the specialist's area of expertise. If I was as concerned about everything as experts thought I should be, I would spend all day worrying and no time getting anything done. Considering that dynamic (which often results in "rational ignorance" by average citizens), it is not at surprising that individuals look to peer groups or ideological leaders for cues on complicated issues.
(I suspect the authors also have an ideological bone to pick, based on the breakdowns they chose -- why focus on "hierarchical individualists" versus "egalitarian communitarians", and mention the hierarchy/egalitarianism and individualist/communitarian axis results in passing? How many other proxies did they look at before settling on those, and why did they reject other possible proxies? These social scientists might be unduly concerned with their narrative and as a result not take methodology as seriously as statisticians think they should [wink, wink -- I know that social scientists tend to take post-hoc analytic methodology more seriously than many domains because they are short on testably predictive hypotheses].)