The evidence itself most often is based on what an authority told us. Authorities exclude evidence, throwing out data they don't like. Then the "evidence" comes to us, pre-packaged and prepped for us to come to the exact same conclusions as the authorities who doctored it (unconsciously, most often).
Authorities rely on the same tricks as preachers when presenting their evidence. They use emotion to underscore their points. They hand-wave a lot in their equations, setting variables arbitrarily, changing terminology, redefining terms, idiosyncratically using accepted symbols. In conclusion no, I don't trust authorities in science. I think science holds on to inherently flawed models way longer than it should, using the excuse about "rational thought" that you made in your post. I think science authorities should be more humble and admit that their model is flawed and not immediately dismiss other theories.
I think scientists have huge priors, in Bayesian terms, and the more entrenched a theory becomes socially the closer those priors get to 1. Then no amount of conflicting data will change their minds. So geologists attacked Wegener's continental drift theory for decades, using all sorts of disingenuous arguments to discount his reasoning. Was that rational? You define it as such. I see it as emotional gossip.
I think the evidence used to support current models is shaky. So in engineering you use a safety factor of 2 or more, which can cover up a lot of contrary evidence, for example.