That's not why people distrust "The Science". At least in the US.
The reason some people distrust it, is because some politicians have figured out the best way to stay in power is to create wedge issues out of everything, blame the "rich" "elites" at these agencies for everything that's wrong in their constituents' lives and seed distrust about everything claiming they're the only people who can fix it.
I don't think so. I think the phrase "trust the science" has caused massive damage, and that's not been individual politicians. Repeatedly changing the story, and saying clearly unknown things as absolutes over and over, and collaborating with social media (and traditional media) to wipe out conversation about these things - that later change anyway - is what's done it. People in the US seem already slightly tilted away from authoritarianism. They're sensitive to this stuff.
The reason some people distrust it, is because some politicians have figured out the best way to stay in power is to create wedge issues out of everything, blame the "rich" "elites" at these agencies for everything that's wrong in their constituents' lives and seed distrust about everything claiming they're the only people who can fix it.
FUD as a policy is very powerful.