> ...and flat earth theory also has a lot in common with religion.
I wouldn't say so. At least not in the epistemic/anti-epistemic way that parallels climate-change denialism. Most religions make a lot of unfalsifiable claims. Since opponents cannot conclusively falsify those claims, it gives religious adherents an epistemic place to hide and claim personal religious experiences, etc.
Most religions have not, in the main, been conclusively refuted, since they involve events that happened thousands of years ago, and even when something is shown to have not happened, the adherents have good precedent for claiming that a given portion is allegorical. Since religious interpretation is rife with different viewpoints, they'll even have a respected theologian to point to who called it in advance.
Flat-eartherism is a horse of a different color. It makes a bunch of falsifiable predictions, which have subsequently been falsified many different ways. Then its proponents just ignore the evidence and keep on believing their viewpoint anyway. Epistemologically, climate change denial has a lot more in common with this than it does with religion.
I say this as an anti-theist. I don't have much good to say about religion, but I'd rather deal with someone who believes things which can't be proven rather than someone who believes things that have been conclusively disproven. Religious people are in that way a lot like anyone else. They aren't as deluded as someone who can look at clear evidence and simply ignore it.