Actually, even a deflated balloon (and straws) aren’t allowed in Animal Kingdom. They’re choking hazards for the animals.
Have you ever been to a really crowded place like an outdoor mall or a parade where people have their animals on leashes? They make life hell for everyone trying to walk nearby them. It’s no wonder Disneyland bans non-service animals.
Again, I like to think the creepy factor is the big reason for this policy, but it could also just be that they don’t want some dude wearing a Mickey Mouse mask acting like a park rep.
How large is “large?” If you have to ask…it’s probably too large. This is also likely done to curb commercial photography on-site.