The implicit, and false assumption in the anti-anti-anti-science position is that there is some better way of convincing the anti-science group to change their minds, for example by framing climate change in terms more congenial to political right-wingers. This is pretty clearly wrong. Long experience has shown that nothing is going to shift the right on an issue that has become a tribal shibboleth.
But if the vast majority are only at most moderately tribal, they may still be eventually reachable by strong logic and evidence. And, a strong majority can still usually get what they want over the long run, at least if it's something they feel strongly about.
So perhaps a single, credible refutation within a news article isn’t likely to convince people to change their views. But other research suggests that a constant flow of these kind of corrections could help combat misinformation. The theory is that the more frequently someone is exposed to information that goes against their incorrect beliefs, the more likely it is that they will change their views.
“It’s possible there is something to be said for persistence,” Reifler said. “At some point the cost of always being wrong or always getting information that runs counter to what you believe is likely to outweigh the cost of having to change your mind about something. We need to figure out what is the magic breaking or tipping point, or what leads people to get to that tipping point. I think we’re just scratching the surface.”
He pointed to a 2010 paper in Political Psychology by David P. Redlawsk and others, “The Affective Tipping Point: Do Motivated Reasoners Ever ‘Get It’?”
The researchers sought to determine if a tipping point exists that could cause voters to abandon motivated reasoning and view facts in a more rational way.
“We show experimental evidence that such an affective tipping point does in fact exist,” they write. “… The existence of a tipping point suggests that voters are not immune to disconfirming information after all, even when initially acting as motivated reasoners.”
This tipping point is far from being identified, but it’s encouraging to think that repeated efforts to debunk misinformation, or to simply to spread the truth, may have an effect.
At least if they're not the very hard core (and only a relatively small minority are very hard core), it's not clear that the're impervious to logic, evidence, science. We should keep that in mind.
As Krugman points out, what matters is not the impact on the anti-science group themselves, but on the attitudes to that group among others. The recent measles epidemic didn’t have much of an impact on anti-vaxers, as far as I can see, but it certainly changed attitudes towards them, greatly reducing sympathy for their desire to pursue their deluded beliefs regardless of the risk to the rest of the community.