Another purpose of obviously false propaganda is for detecting conformance. If propaganda says that 2 + 2 = 5 and a citizen states that 2 + 2 = 4 then that citizen can be red-flagged by the state apparatus (or others within the in-group).
I remember listening to someone point out (I think it was Sam Harris) that what all ideologies and religions have in common is that they must have, somewhere, a very strange idea that everyone in the religion must accept. One that clearly goes against common sense and experience.