Prior to last year, I hadn't seen any real dogs in the theme parks. But on my trip last November, I saw several dogs in each theme park, on multiple days. Some of them may have been legitimate service dogs, but I doubt that all of them were. Many were small breeds (poodles, chihuahuas, etc.) Could they all have been service poodles -- maybe, I don't know.
There has been a drastic increase in the amount of dogs in the theme parks, from the zero I'd observed on all my previous trips, to seeing multiple dogs daily on the most recent trip. If this many people really need a service dog, it is puzzling why the need suddenly began last year.
While I haven't seen a Disney policy specifically stating that emotional support dogs are allowed in the theme parks, I also haven't observed any efforts to screen out non-service dogs from entering the parks.