@steve , except for one niggle, @sklaing is entirely correct here.
I'll dispense with the niggle first: Where she says Democrats, I would say people on the left. Where she says Republicans, I would say conservatives. Both major parties are increasingly losing legitimacy, as we see with Democrats and Hillary Clinton, as we see with Republicans and Jeb Bush.
Now, to what this thread is actually about. First, scientific method, i.e. positivism, has its own issues with what knowledge it considers acceptable, what forms of knowledge it considers acceptable, what methods of inquiry it accepts as legitimate, and an arrogance that it has a right to determine that legitimacy, when it relies on an unverifiable theory of truth (hint: there is no theory of truth that holds water, full stop, period).
Second, even within the positivist paradigm, its practice seems severely flawed. One of the very basic principles of positivism--the reason science should be transparent--is replicability. Increasingly, studies are not replicated; apparently doing so is too boring. But without replication, there are all sorts of problems which I hope are sufficiently obvious I don't need to dwell on them. Further, peer review turns out to be a crock of shit, as has become increasingly obvious in the past couple years. The scandals of open access journals are actually not so much about open access as they are an indictment of the peer review process itself. Then there are all the traditional concerns about peer review, that it serves to reinforce the consensus rather than enable challenges to it, for example.
Third, even within the positivist paradigm, there are a number of controversies in which it turns out that studies funded by corporate interests are more supportive of the corporate agenda than studies that are independently funded. This includes cell phone radiation, bee colony collapse syndrome, and genetic engineering. Most frightening of all in this space, pharmaceutical companies have increasingly turned to private labs apparently because they more reliably return the results the companies want than university researchers. And even university researchers are pretty awful about conflicts of interest. (The scuttlebutt I hear is about federally-funded marijuana research accordingly tailored to suit the DEA agenda.)
Skepticism is intrinsic to scientific method. But first, what we're seeing is cynicism; and second, the safeguards necessary for keeping science honest are proving woefully inadequate. And third, perhaps most important of all, instead of trying to understand why people are so skeptical of science, we cast aspersions upon those people--in effect an ad hominem. Scientific and medical authorities need to be repairing their relationships with the general public but largely refuse to do so.