Belief in disbelief:

One of our neighbors in Tisvilde once fixed a horseshoe over the door to his house. When a mutual acquaintance asked him, 'But are you really superstitious? Do you honestly believe that this horseshoe will bring you luck?' he replied, 'Of course not; but they say it helps even if you don't believe it.'

— Niels Bohr

(Note: This is often retold with Bohr himself as the one with the horseshoe, but this quote appears to be the authentic one.)

I wonder how common that is, believing that you don't believe something but acting in a way that implies more belief in it than you acknowledge. One other example I experienced recently: For whatever reason, my mom had a homeopathic cold remedy lying around. (I think a friend gave it to her.) She and I both had colds recently, so she suggested I try some of it. The thing is, she gives full assent to my explanations of why homeopathy is both experimentally falsified and physical nonsense; she even appeared to believe me when I looked at the ingredients and dilution factors and determined that the bottle essentially contained water, sugar, and purple food colouring. But even after that, she still said we may as well try it because it couldn't hurt. True, it couldn't hurt... but "it can't hurt" doesn't sound like really understanding that the bottle you're holding consists of water, sugar, and purple.

Another instance may be former theists who still act in some ways as though they believe in God (an interesting mirror image of current theists who don't act as though they really believe what they profess to believe), though in my experience many of them consider it to be bad habit they're trying to break, so I'd be less inclined to call it belief in [dis]belief, I'd take that as something more akin to akrasia.