On the other hand, there is a large contingent - probably the vast majority - for whom no amount of rigor or proof would be sufficient. Flat Earthers can be shown evidence for days and reject it all, for instance. Because it isn't really about the facts for most folks.

I also think - and suspect TFA agrees here - that taking lunatics (or, more likely, the intentionally dense) seriously emboldens them, and lends their ideas the unearned merit of your efforts. Sartre had something to say about that, too.