Term for choosing to believe a falsehood
Solution 1:
Another word that springs to mind is
doublethink from George Orwell's 1984 for accepting contradictions and falsehoods as a technique of self-indoctrination, which itself is a good word I think.
Solution 2:
Self-deception is the act of hiding the truth from yourself.
Solution 3:
Not quite one word but close enough, for people that really want to believe in something even though they don't think that it is true, we could say it's a "foolish hope" or a "fool".
For people like fortune tellers that doesn't actually believe what they were telling others to believe, we could call them a "hypocrite".
For people that actually truly believe their false pet theories, and doesn't in any bit doubted its falsity despite contradictory evidence, we could say they're "misguided" or "deluded".
Solution 4:
There is a phrase wishful thinking used to describe a concept that is highly unlikely, but you would oh-so-hope could be true
the attribution of reality to what one wishes to be true or the tenuous justification of what one wants to believe