Despite the language in the coverage, it’s not science as a method that people are losing confidence in; it’s scientists and the institutions that purport to speak for them.
Gauchat’s paper was based on annual responses in the General Social Survey, which asks people: “I am going to name some institutions in this country. As far as the people running these institutions are concerned, would you say you have a great deal of confidence, only some confidence, or hardly any confidence at all in them?” One institution mentioned was “the scientific community.”
So when fewer people answered “a great deal” and more answered “hardly any” with regard to “the scientific community,” they were demonstrating more skepticism not toward science but toward the people running scientific institutions.
With this in mind, a rise in skepticism isn’t such a surprise. Public skepticism has grown toward most institutions over the last several decades, and with good reason, as a seemingly endless series of scandals and episodes of dishonesty have illustrated.
In fact, given that Americans have grown broadly more skeptical of institutions in general, it’s not surprising that conservatives are more skeptical of scientific institutions than they were almost 40 years ago. What’s surprising is that liberals have grown less skeptical over the same period. (Perhaps because scientific institutions have been telling them things they want to hear?)
Regardless, while one should trust science as a method — honestly done, science remains the best way at getting to the truth on a wide range of factual matters — there’s no particular reason why one should trust scientists and especially no particular reason why one should trust the people running scientific institutions, who often aren’t scientists themselves.