I agree that, subjectively, it seems like the popular discourse surrounding the nature of science is not exactly philosophically rigorous. And I agree that some people seem to hold quasi-religious views of science.
Maybe I totally misunderstood OP, but it seemed like they were conflating the state of popular discourse with the state of academic philosophy.
As an aside, I don’t think that people are likely to stop trusting in science or the scientific community because of the state of discourse surrounding science. I think that people are much likely to distrust science simply because they don’t like certain findings or it’s not politically aligned with them, imho. At least in America.