We started going when DS was 4 and only knew the Winnie the Pooh stories. It did nothing to diminish his enjoyment.
By the next year, he had seen the new Pooh movie and Lady and the Tramp. (Thus ready for Tony's for lunch in the Magic Kingdom.)
Now at age 8, he has seen the first two Toy Stories, Cinderella, Monsters Inc and Monsters U, A Bug's Life, 101 Dalmatians, Frozen, Big Hero 6, Inside Out and the Aristocats.
He still adores it. And loves to meet the characters, even when he doesn't know the movies...