> public has lost a lot of trust in Science because research papers have been used to push political agendas, which can then never be questioned because doing so means arguing with a supposed peer-reviewed scientific consensus
The public has lost trust in science because 10 to 30% of it is scientifically illiterate [1]. (Tens of millions of American adults are literally illiterate [2].)
That's what lets activists and politicians cherrypick bad science that supports their position or cast a scientific consensus as unquestionable.
[1] https://carsey.unh.edu/publication/conspiracy-vs-science-sur...
That's certainly true but I think there's also a very real issue as described by GP. Research gets cited in a political setting as a rhetorical tool. That cycle does a lot to erode trust in the establishment because it incentivizes non-scientists (who are otherwise uninvolved) to behave as though the process is a partisan effort to be interfered with for the benefit of one's "team" rather than an objective pursuit to be funded at arms length for the betterment of society at large.
Obviously reproducing results as part of peer review is not a workable (or even coherent) solution. I don't pretend to have any idea what a solution might be. The obvious issue is that academic publications were never intended as political tools and should not be made into that.
On several occasions I've had interactions with laymen where I found myself thinking "if only you hadn't had access to pubmed and way too much motivation we'd both be better off right now" yet I firmly believe that free and open access to information is a huge net benefit to society on the whole.