The extreme examples are people like young earth creationists or global warming deniers, who can be shown giant reams of evidence that just seem to slide off of them. It just makes no effect. They create elaborate, self contained conspiracy theories to prop up their position; climatologists are engaging in a massive conspiracy, for instance, or God made the earth to look just as if it were billions of years old, but really it's not.
Now imagine that most people aren't that extreme, but do many of the same things to notably lesser degrees. I'm sure I do it sometimes. We find ways to argue with inconvenient facts we don't like on an emotional level. We find ways to ignore evidence that doesn't suit our worldview.
I'm not suggesting that getting the facts out there is useless and that we should stop, I'm just saying that we account for human nature at the same time. The human brain is not some perfectly rational, reasonable instrument. Especially in an emotionally charged environment -- like a discussion of autism with parents of autistic children -- I think we need to expect that most human brains will be driven by emotional needs first, with logic serving as a slave, not a master.