The ones that always blew my mind were the devout creationists that work as archeologists. They just refuse to believe any archeological evidence of anything older than the age they believe the planet is according to their faith. Anything that appears to be older than that they believe was just created when the earth was born.
I could never reconcile how it was logical that the earth was created with fossils that appear to be millions of years old just for our entertainment. Yet, somehow they had no problem accepting that.