No, I understood, my reply was meant as a disagreement. You're defining "extremist" as someone who ignores evidence that counters their beliefs, but that isn't what the word means, is it? Or rather I've never seen someone define it that way before. You could use words like "stubborn", "closed minded", "ideological" or whatever to describe such people but "extremist" always means someone whose views or actions depart seriously from the mainstream.

In particular, most people recognize the possibility (at least theoretically) that someone can be both an extremist and also correct. Whereas by your definition that's impossible.