They don't necessarily ignore evidence but when they see it, they think they know that the evidence is either false or incorrectly interpreted.
In fact, I'll wager that AV and Skywriting would not change their minds or admit that their beliefs are incorrect no matter the level, amount, or kind of evidence. You could have them travel back in time, find out that Jesus didn't do the things that the Bible claims he did, and they still would not believe it. They'd hand-wave it away it as either a hoax, some miscalculation, a case of mistaken identity or some other logic acrobatics. You could satisfy every single kind of ridiculous request of evidence such as crocaducks, dogs being born to cats, and they would still not believe. It does not matter what they see, hear, touch, or sense with any of their senses, their worldview is already frozen and therefore stagnant. And most curious of all, they see all these descriptions of their worldview as valued and treasured wisdom. It's surreal.