You can’t buy chewing gum in any of the Disney destinations, anywhere in the world. You won’t find it for sale in any of the parks, in any of the hotels, or in any of the shops. Disney doesn’t explicitly ban it — if you want, you can bring your own; practically, how could they stop you? — but it is strongly discouraged.
Why? That’s obvious: once dropped, it makes a mess that is tough to clean up. Disney’s in-park cleaning operation is legendary. Cast Members are not only obliged to pick up litter whenever they see it, they are trained to do so without stopping moving, so as not to draw attention to the mess. Naturally, they can’t do that with gum, which adheres to concrete quickly and takes a while to scrape off.
They truly do think of everything.