Trust in science has dropped by 25% since 1970 among those who identified themselves as conservative. This is the conclusion of Gordon Gauchat’s paper that appears in American Sociological Review. According to the study: 

To summarize the main empirical findings, this study shows that public trust in science has not declined since the 1970s except among conservatives and those who frequently attend church.

 

Interestingly, conservatives were far more likely to define science as knowledge that should conform to common sense and religious tradition. Relating to the second pattern, when examining a series of public attitudes toward science, conservatives’ unfavorable
attitudes are most acute in relation to government funding of science and the use of scientific knowledge to influence social policy. Conservatives thus appear especially averse to regulatory science, defined here as the mutual dependence of organized science and government policy.

Apparently there has been little or no shift in the trust of science among those who self-identify as moderate or liberal.