A new study in the American Sociological Review examined how conservative trust of science has declined over the years. The problem is more pronounced among the educated:

Conservatives with high school degrees, bachelor’s degrees, and graduate degrees all experienced greater distrust in science over time and these declines are statistically significant. In addition, a comparison of predicted probabilities indicates that conservatives with college degrees decline more quickly than those with only a high school degree.

One possible explanation:

"In the past, the scientific community was viewed as concerned primarily with macro structural matters such as winning the space race," Gauchat said. "Today, conservatives perceive the scientific community as more focused on regulatory matters such as stopping industry from producing too much carbon dioxide."

Kevin Drum wonders why moderates are also skeptical of science:

Until recently, moderates trusted science significantly less than either liberals or conservatives. Is this because moderates have always viewed science as a politicized enterprise, something they're especially sensitive about? Or because moderates are just generally less engaged with elite institutions? Or because moderates have a higher overall degree of skepticism about everything than either liberals or conservatives? It's a mystery.

Nick Gillespie has doubts about the study:

Note the wording of the question, which stresses attitudes toward "the people running these institutions." It doesn't ask whether you think science has changed. It's specifically asking about the folks wearing literal and figurative lab coats who are running joints like the National Science Foundation, testifying before Congress, appearing on The Tonight Show while forecasting famine up the ying-yang and praising coercive population control measures, and who often end up being totally wrong about everything.