Few people who utter the phrase "trust the science" are scientists or care about science.

In that phrase, "the science" refers to the enforced narrative.

It means “I would rather trust the results of a scientific process than trust politicians.”

That's the thing, "the science" doesn't come from a scientific process, it comes from a political one.

That is the ideal, sure. In practice though, science is whatever scientists do.

And as seen here, sometimes scientists don't actually follow the scientific method, they fall trap to entrenched interests and other biases.

The people that tell you "trust the science" are not usually suggesting you get a PhD and study this yourself. They are actually suggesting you trust the scientists - which may or may not be good advice based on the field (e.g. trusting physicists, climate scientists, virologists: good; trusting dieticians, Alzheimer's researchers: possibly bad).