If climate scientists can’t convince level 2′s and also level 3′s, people who are looking at the arguments carefully, reading the primary literature, and analyzing data, then it seems to me that the arguments can’t be that strong (or the confidence levels can’t be that high).
If we state this as a general proposition, that proposition would be:
People are persuaded if strong arguments are presented to them, provided they are intelligent enough to read and analyze data.
Or, since most people acknowledge that strongly biased people can ignore or distort data to affirm their preexisting beliefs, we might simply state it as "Intelligent people are never strongly biased."
This is the "Well you haven't convinced me" fallacy: the idea that the responsibility of scientists is to convince everyone, and if a denier withholds their approval of a line of argument, then it is those who argue that have failed -- failed to persuade.
Let's consider briefly some of the ideas that have had intelligent and articulate defenders over the years. Totalitarian communism. Eugenics. White supremacism, colonialism, absolute monarchy, religious fundamentalism. All have had aggressive and well-read advocates, as do contemporary anti-science movements like the anti-vaccine movement and creationism.
Sadly, there is no evidence in support of the proposition that intelligence is a protective factor in the embrace of ideological filters. Nor is it true that bias and self-justification -- concepts that has been extensively studied and found to be incredibly powerful -- deprive us of the ability to read and analyze data; the analysis in question just turns out not to be very good, cherry-picked and misattributed and otherwise given a good working over by the subject's confirmation bias.
If anything, it's easier to become attached to an ideology and defend it from all comers when one is educated and facile with the source material. The test of an argument in science is whether it can stand up to scientific critique, not whether it can persuade people who have already made up their minds and invested a considerable portion of their self-regard in their dissident position.