I can’t speak for all members of the GOP, but I can speak for myself. As for myself, my trust in scientific institutions is at an all-time low, but my trust in legitimate and honest science is at an all-time high.
I know this is hard for many people to understand, but scientists are not gods. They are not even remotely perfect. The best physicists that graced the face of the earth were not much smarter than you or I.
Putting your trust in any scientific institution is insane. The people who run these unions are just as susceptible to corruption as any other institution. That means that they can be influenced by money or prestige to falsify results. That means they will intentionally manipulate the peer-review process to obtain results they think are favorable to their interests. That also means they are likely to engage in conflict among each other, and set their professionalism aside to destroy the careers of the people around them.
Putting your trust in science is wise, as long as your definition of science is the true definition of science. Science is the pursuit of knowledge through the exposition of error. It is based on infallible logic and reason, and has no motives or intent. It is a mute, dumb beast. Scientific advances come over time spans of decades, not weeks, months, or years. New scientific thought is instantly questioned and subjected to an unending series of challenges. Scientists who work in true science do not think that our current understanding of science (which is different than true science) is correct, and are busily engaged in finding out why we are wrong.
Putting your trust into the things scientists say is not a good idea either. The current understanding of science, as you should see above, is not true science. It is wrong in many ways, and in surprising ways. In physics, we do not accept mere theory as fact. We only accept actual observation as fact. Theories seem to be pretty good at explaining why we see the things we see, but none of them are perfect. It is in the discrepancy between observation and theory that physicists spend their time. If you are a physicist, yes, you do have to understand what physicists currently believe is correct science, but you must also simultaneously reject it as incorrect. If you believed current science outright, then there would be no motivation to look for better or more accurate theories.
I know this is hard to accept for many people. You have been told to believe in the Big Bang Theory, in Evolution, in Climate Science, and all of these things, because groups of people with PhD’s after their names and who sit on important-sounding boards and councils say so. That is not science. That is religion. Think about it. The only reason why religion exists is because some man with an important title such as Prophet or Apostle or Priest said you should believe something.
Instead, you should treat every scientific article and discovery with deep skepticism. Until you can follow the logic and explain every step with solid, unshakable reasoning, you should treat it the same way you would treat your horoscope. And even then, you should be looking for where your logic and reason went wrong, and be actively pursuing every shred of evidence that seems to contradict any part of your reasoning.
Do me a favor. If you encounter a scientist that asks you, the non-scientist, to simply trust them, in particular with matters conce, can you do me a favor and treat them the same way you would treat a con-man?