In English particularly, people associate "thou" with the King James Bible and similar Christian texts ("Our Father, thou art in Heaven…") and might reasonably assume that if "thou" was used to address the literal God, it must have been the formal pronoun – but the familial, informal one was used exactly because of the "father" association! (OTOH there certainly are languages with a tu/vous distinction where children were expected to "vous" their own parents – not sure how much of a thing it is these days).

Another fun thing is that calling someone you don't know "thou" used to be an intentional insult ("you're not worthy of being called 'you'"), something that might be missed by a modern reader of Shakespeare or other EME texts.