In part, maybe, but the issue is a little more subtle. People who go all anti-vaxx or anti-GMO are not just saying that science is wrong. Hell, they often try to twist the science into supporting their point. What those people feel is that government and corporations are trying to hurt them. You don't see heated arguments about whether vaccines interact with this or that metabolic pathway. The issues is whether vaccines will hurt your kids, and whether government is forcing you to do something bad to yourself. It's not about facts - it's about trusting authorities that they're not trying to exploit and harm you.

What I always find interesting reading the comments sections in newspapers, is that certain groups of people deny and dismiss the hard science of climate change, yet the same people seem to believe the very poor science of economics as if it is some kind of proper science.

I'm confused then -- why, in terms of correct vs. incorrect outcomes, does skepticism work out so well for those trained in the methods of science, but so poorly for those who are not?

Because you can't just say "I'm sceptical" and expect to magically arrive to the correct conclusion. You have to know exactly why you're sceptical about something. Being "trained in the methods of science" gives you mental habits of analyzing known facts and conclusions instead of just doubting anything which you don't like.

>Because you can't just say "I'm sceptical" and expect to magically arrive to the correct conclusion.

Yes. The idea that "the worldview based on science alone has reaped what it has sown," seems a little silly in this context, as skepticism by itself is not what science promotes. If the skepticism was rooted in science, we might see many other beneficial behaviors associated with scientific method accompanying the skepticism. But we don't, indicating (to your point) that the skepticism stems from distrust for authorities in general, not from middle-school chemistry classes.