Earlier quoted context omitted.
Science in America tends to be practiced in universities, and universities in America are no longer open to the free exchange of ideas. While it may look like the public is losing faith in science, it's actually the public losing faith in the platform on which science is practiced: academia. If we want the public to regain faith in scientific findings, we need to fix academia.
I agree to some extent, but the whole "culture war" dimension of this question is far less important than people think. It has much more to do with corruption and broken incentive structures than with the identitarian critiques being pumped out by poorly-funded humanities departments. Until getting so much attention recently, they were at worst a minor check on what really has been an undeserved intellectual hegemony…
We need to clean our own house. I can't even keep track of how many brilliant people I personally know who have left academic research. It's really very tragic and our duty as citizens should be to ignore all the petty distractions and focus on doing what needs to be done. If the institutions are lost and beyond reform, we need to work on building new ones that work for us. The current crises could be great opportunities for this.