Ok so the original formulation for "the moon is made of cheese" idea comes from a metaphor for credulity in a proverb from the High Middle Ages.

"... the Servian tale where the fox leads the wolf to believe the moon reflection in the water is a cheese and the wolf bursts in the attempt to drink up the water to get at the cheese; the Zulu tale of the hyena that drops the bone to go after the moon reflection in the water; the Gascon tale of the peasant watering his ass on a moonlight night. A cloud obscures the moon, and the peasant, thinking the ass has drunk the moon, kills the beast to recover the moon; the Turkish tale of the Khoja Nasru-'d-Din who thinks the moon has fallen into the well and gets a rope and chain with which to pull it out. In his efforts the rope breaks, and he falls back, but seeing the moon in the sky, praises Allah that the moon is safe; the Scotch tale of the wolf fishing with his tail for the moon reflection. — G. H. McKnight

Overall, this refers a gullible person -remember, the original meaning of this is to inform about credulity- who sees a reflection of the Moon in water and mistakes it for a round block of cheese. So, no, no one ever seriously believed that the moon was made of cheese. That's like full-on believing that a rabbit would lose in a race against a tortoise. The reference to the moon being made of cheese is just as a folkloric motif among many countries' popular culture.