Julie Andrews does not own the rights to Mary Poppins in any way, shape, or form. Neither do Amy Adams, or Johnny Depp. In legal terms, your likeness as a character is not the same as your likeness elsewhere. That would be like saying that there could be no other voice given to Mickey Mouse than Walt, because he owned the right to voice Walt.
Merchandise can be a bit different, but Disney can have as many theme park actors/actresses play Giselle, Jack Sparrow, and Mary Poppins as they want. When they bought the rights to the books of Mary Poppins, they owned the intellectual property. When Julie Andrews signed on, she received some stipulation for her to play the character. When Johnny Depp signed on, he probably also agreed to some royalty amount for merchandising the Jack Sparrow likeness, etc. But, he has no control over the use of the character in the park.
Amy may have originated the character, but she does not own it.