If there were mass worship of science and deference to critical thinkers going on, don't you think we'd have cut back on consumption of the planet's resources to fix the problem of global warming, since that's what the experts have been recommending for years? That hasn't happened in the US or China, the two biggest polluters.
In the US certainly, there's rampant anti-intellectualism and paranoia, including distrust of experts that's based not on healthy skepticism but on arrogance, individualism, and infantilization. The only connection between that decadent culture and science is that science supports the technological applications that infantilize the mass of consumers.
But if you ask a child whether she trusts scientists because they're smart or whether she thinks she knows better, she may just as well answer the latter, depending on how she's been raised. Consumers think they know better even if their education has been substandard because of deregulation, the corporate capture of the democratic government, the rise of antisocial neoliberal or right-wing ideologies, and so on.