Science is different because it typically doesn't have the ten-fold margins of safety that are customary in engineering. Imagine if "the bridge is safe (p < 0.05)" were the standard!
People have confidence in engineers because they get daily feedback that things have been done well enough. Most people can't do a finite volume modeling of a bridge support under load, but they can observe that they have driven over the bridge five hundred times, and many thousands cross every day, and everyone is okay. (This works until we get into rare events like earthquakes.)
This demonstrated competence, like Yelp reviews of dentists, helps engineering as a discipline maintain quality control. There is pressure from society, constantly, to get it right.
What scientism gets right is that science needs to be celebrated, because if science ho-hum-whatever, the societal pressure is off, the funding is down (spending, instead, on transient short-term pressures rather than accumulating knowledge for humanity), and it works less well.
What it gets wrong is that the pressure needs to be "do the best science!" not "science is the best!". And that is observable to an extent. "You wouldn't understand so I won't tell you" is a terrible way to demonstrate that one is holding one's ideas up to rigorous testing against reality. "You might not understand but I'm going to tell you anyway, and every step you don't understand can in principle be looked into until you see how reliable the whole inference is," demonstrates the point nicely.
And it's an extra layer of defense against "best practices in the field" being rubbish. (We need more defense than that. This is something that I don't think science has quite figured out sociologically. Every time I switch field to an extent I end up surprised by some aspect of what gets accepted as good evidence.)
Whether or not one "trusts science" generally doesn't come up when one is talking about the binding affinity of PDF for PDFR. It comes up when one is told to wear a mask, use statins, stop using CFCs, eat carbs instead of fat, provide tax breaks for electric cars, etc. etc.--areas where it impacts daily life in substantive ways. Some of these sorts of things are awfully inconvenient, so sociologically it's good to have some cheerleading to make doing the non-obvious-but-seemingly-needed thing easier. But some of these things were wrong and we would have had a better chance of catching it at the time if the cheerleading was "look, this is how we (think we) know!" not "we believe science!"