...I wish I knew. It's really hard to tell what other people believe at a fundamental level, and there's certainly a humorous undertone to nearly all flat-earth evangelism I've encountered. But what's telling is that I've pretended to be a flat earther myself when mocking climate sceptics. In terms of the basic trust in many other people OR basic competence in the realm of physics required not to hold a belief, climate change scepticism and round-earth scepticism actually seem fairly close to me. And I'm sure there are sincere climate sceptics.

Flat-earthism is a noncontroversial and extreme example of a belief that gets less believed when its proponents have the full benefit of free speech, but I think there are many more like it.

I mean, it certainly looks flat (or at least, not curved) to me when I look out my window ;)

it's pretty rare for an ordinary person to have the opportunity to directly observe the curvature of the earth. I personally don't notice it when I fly commercially. you can indirectly observe it with binoculars on the beach by watching ships (dis)appear over the horizon, but a) you have to recognize the implication, and b) this can be confounded by a mirage/shimmer effect.

it's not hard for me to imagine that some extremely skeptical people might doubt that the world isn't simply how it looks: flat.

We have satellites imaging the Earth as they orbit it. We have astronauts on the Space Station. People fly and sail all over the world. Maps and GPS work based on the Earth's curvature. There's no conspiracy by NASA or whoever which could possibly keep the truth from hundreds of millions of people who know for fact the shape of the Earth.