"Bats in the belfry" - vernacular for not quite right upstairs.

See also:

a screw loose
not the sharpest tool in the shed
a kangaroo loose in the top paddock

and, of course, the title phrase.

InfoWars: "Brainchild" of Alex Jones, leading conspiracy theorist.

Please note:

This is not lampooning people with a genuine mental disorder. That is not something I'd ever want to do. It's more poking fun at clinically sane people who choose to believe the most outrageous nonsense.

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