If they're actually engaging in real science

A fundamentalist scientist who's trying to prove evolution isn't real, is not really engaging in science for example, he's engaging in activism for his religion. As a result his method is to starts with the conclusion that evolution isn't real, and then cherry picks all the evidence to support it, and intentionally ignores the evidence in favor of evolution. This method is the opposite of science that starts with evidence and then draws conclusions from it, or lets their original hypothesis be challenged by new evidence.

I have no reason to take seriously scientists who use this circular logic seriously, no matter how many PHDs they have. In an ideal world peer review would be able to spot obviously biased science... unless the peer reviewers share the same religious or quasi-religious views as him. At that point they're more likely to reject him for not being subjective enough towards their beliefs.

When it comes to how why the right doesn't "trust the science" on things like covid and climate change, this is how they're viewing those scientists. They view left wing ideologues as having taken over the science field in order to be soldiers for their ideology, and once the top universities purged non-left wing thinking from peer review, it became nearly impossible for a conservative to reach the type of credentials that the people like Fauci propped out by the government and media do. The idea that you're not allowed to question the science on things like covid, goes against what science is supposed to be, which is something to be challenged and tested.