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I don't think people who say "Trust the science" are saying that science has it all figured out. It's telling people that they should weigh scientific data into their thought process. In reality many people make all of their decisions based on emotions and "feels".
"Trust the science" really came into its full form during the pandemic and was a veiled line in appealing to authority. The CDC, Dr. Fauci, NIH, or any governing body issuing mandates during the pandemic would tell you to trust the science, when in reality they just didn't want people to question their decisions. As it turns out, some of the people questioning school closures or masks were correct! Questioning vaccin…
It's true that some of the people who questioned the science were right, but not because they knew something scientists didn't. A broken clock is right twice a day. If something like that happens again we may need to be more cautious than we were last time. It certainly makes sense to be as cautious as possible until we know for sure how deadly some new disease is. Another side effect is that people took sides and trenched in. When it started becoming clear that masks weren't as useful as once thought (at least for sure cloth masks), the other side refused to admit it. What we should do (but are incapable of) is make the best decision based on the current information and change practices as new information comes in or conditions change.