The generation of distrust of science has multiple sources which seem obvious:
1) Phony, arrogant, self-referencing "science" experts spouting Truths from an environment of philosophical Relativism.If you think of some that I missed, add them in the comments.
2) Obviously bad science, and reports of high percentages of false scientific papers: the continual overturning of "settled science" (nutrition, health, drugs, anthropology, psychology, medicine, cosmology, Quantum Theory, trees of life, "missing links", non-objectivity of AGW (measurement manipulation and computer sims), suspicion of particle science conclusions; unfalsifiable String Theory; irrational claims by Hawking, Krauss, Dawkins, Dennett, et. al., irrational claims by brain neurological mind theorists).
3) Political enforcement of certain questionable, unfalsifiable "sciences".
4) The use of unfalsifiable sciences for Leftist political redistribution of global assets and wealth.
5) The failure of philosophical materialism, both in logic and in religion.
6) The top-down diktat of unfalsifiable, untestable evolution as a Necessary Truth of existence: direct political and legal attack on religion. "Theory AND Fact" is obviously false, and reflects onto actual legitimate sciences which actually do have both theory and contingent facts.
7) The denial of any essence inherent in "life" which differentiates it from death, or from material mineral existence which is driven completely by the deterministic entropic four forces of physics.
8) The insistence that the human mind is a purely physical entity.
9) The denial of choice and agency in humans (humans are subject to pure determinism of the four forces of nature and initial conditions regressing back to the Big Bang).
10) The failure of reputable sciences to defend themselves from non-falsifiable, non-empirical faux science, and to de facto capitulate to them instead. (E.g.,Modern Biology could and should divorce itself from evolution; Astronomy should divorce itself from Cosmology; Anthropology has already divorced itself from being a science).
11) The misuse of science in the killing of human embryos - lack of ethics.
12) The misuse of science in the manipulation of living human embryos, resulting in deformation and death.
13) General Atheistic lack of consistent, coherent moral principle. Plantinga points out that although Christianity and Islam are polar opposites, they are closer together than to Atheistic "Naturalism" (Philosophical Materialism). The religious distance from Atheist determinism is an unbreachable chasm which evolution faces from the side of Atheistic Determinism. This failure of an illegitimate, non-falsifiable, non-testable, Appeal to Authority "science" projects onto all legitimate objective empirical sciences, which do nothing to distance themselves from the illigitimacy.