But you don't trust your dentist solely because they say "I'm a dentist!". You also check (1) customer testimonials, (2) make sure they have a DDS degree, (3) can check that they're licensed, etc..

(1) is a key factor because it reduces the instance of ego-driven back-patting or authority-over-results takeover, both of which are big and common failure modes in human behavior.

You can check to make sure your scientist has a Ph.D. and that the research they publish is peer reviewed, but you don't find Yelp reviews saying, "Correctly predicted warming in the Yucatan Peninsula to within 0.3C with five year averaging, and so friendly and welcoming! *****"

The corresponding quality check for science is openness. You can't, as a non-expert, evaluate the science. You can as a non-expert evaluate the performative aspects of the method. "Showed results, engaged with contrary ideas, citing literature and data to indicate why those ideas are likely mistaken. *****"

I don't think the main problem with scientism is arrogance decreasing trust--lots of things are accomplished with bluster. I think the main problem is that it is an excuse to think less carefully and become less attentive to evidence.