I think it's a feedback loop at this point, but as for "which institutions", the media and the academy are pretty prominent institutions that have largely come to describe themselves as activist institutions, including making arguments like "objectivity props up the status quo". Obviously these aren't monolithic institutions, and you still have a lot of variety within (especially the academy) with respect to the degree to which they've become progressive orthodoxies.
> The problem is that when these questions are answered "the right" just dismisses the answers as biased.
Again, I posit that's because the media and the social sciences have a track record of progressive bias. If they made a concerted effort over time to demonstrate good faith and a commitment to the truth wherever it leads (as opposed to outright identifying themselves as activists, although their honesty is worth something), I think far fewer on the right would reject a given claim as 'biased'. Even if I'm wrong, it must be something. There are a lot of people arguing that it's hopeless to interact with the right because they're fundamentally worse people or something, but clearly we haven't always had such a large contingent of "the right" who have completely divorced themselves from mainstream epistemology, so something is driving this change, and there's no reason to believe we can't stall or even reverse the phenomenon.
