I don't think this is an accurate characterization of things. Most people I know believe in climate change, but very few of them could cite any facts or graphs or science that convinced them really. They believe it because people on tv who they trust told them it was true.
I'm not saying this is bad, we should trust experts on topics without expecting every single member of the population to get bogged down in the gritty details. I myself do believe in climate change and vote for democrats. That said, it annoys me when people act like everyone who believes in climate change is a genius who knows science and isn't blinded by ideology while the deniers are cavemen or religious zealots too dumb to get it. Like it or not, it has become a political issue and people on both sides are largely just following their own side, not looking deeply into the findings and methods of scientific studies to decide for themselves if they agree with the researchers.
One time, I saw a graph of temperature over time. That's it. Nobody has ever tried to show me any other theory or evidence. Has anyone ever tried publicizing the science? I take issue with the "science has failed so now we have to be irrational" story because I am not convinced that the science has ever been tried.
There are a lot of people who don't fit that category, and if they are to be persuaded at all, it won't be by the means that are used to convince the scientifically literate. For the illiterate, they might well be tipped by one summer's weather or one hurricane's damage. That's bad science, but the voting booth doesn't care whether your reasons are sound or not. The New York Times is reporting on policy as well as science: what people are going to choose to do.
In that sense the statement is accurate. Those capable of being convinced by science are convinced; those who are moved by incorrect evidence have just received a big wad of it. The only ones who haven't reached the correct conclusion are driven by ideology, and won't be convinced by any evidence.
We can bemoan the fact that so much of policy is decided on bad grounds, but that seems to be a fact of life. Most people don't understand science, and manufactured doubt can be used to sway them from the conclusions reached by science. If you care about getting things done in a democracy, you have to take them into account.
That doesn't justify using the science badly, but that's not what's happening here. They're just reporting on the mechanisms by which people have reached their conclusions.