Flat earthers have zero influence on the development of physics, and their ideas don't matter to anyone except themselves and a few opportunistic journalists.

This is not true in the social sciences where it's very hard to do physics-grade research, especially given that the social sciences are very politicised, and research is often done to prove a political or moral point.

So in practice our understanding of personal and social/political psychology is pre-Copernican. There's a lot of moralising - which you will agree or disagree with, depending on your predisposition - but very little high quality research into the way that moral and political decisions are made individually and collectively.

We're left with a mythology of free objective democratic choice in politics which is clearly naive and reliably breeds monsters, but as yet there isn't a better model of choice to replace it.