"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 vaccine safety for young men was and is correct, as long as there were not comorbidities. The people or institutions that were yelling "trust the science" the loudest were indeed saying that they had it all figured out and that anyone that questioned them was wrong.
"Trust the science" became a campaign slogan during the pandemic, and fell into the same realm as "defund the police" or "trust all women".
So yes, "trust the science" does mean what you said that it is a process that should take data new and old into account. However, the sad thing is it was co-opted by people who used it as a cudgel to silence anyone that didn't toe the line.
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.
I and everyone around me questioned their statements and came to the conclusion they were in fact true. That is what "trust the science" means. It does not mean "do whatever I say" - it means "I am right and you can verify that, so you should probably take what I'm saying into consideration lest we all suffer."
The right wing somehow took "science" to mean "Anthony Fauci"...
"Trust the science" became a campaign slogan during the pandemic, and fell into the same realm as "defund the police" or "trust all women".
So yes, "trust the science" does mean what you said that it is a process that should take data new and old into account. However, the sad thing is it was co-opted by people who used it as a cudgel to silence anyone that didn't toe the line.