To answer the OPs question -
The 'Song of The South' film became associated with what was being developed as a log flume ride for Disneyland Park for two main reasons.
First and foremost was it was a film property that contained great stories, colorful settings, appealing characters, and memorable music which WED / WDI designers always looked for when brainstorming new ride concepts.
It was also a property that had not yet been developed into a Theme Park experience, and leant itself well to the thematic setting.
Folks need to keep in mind that during 'Splash Mountain's early development in the mid 1980s, Disney did not have as many films and characters as it does today to play around with.
These were the days before 'The Little Mermaid', 'Aladdin' and 'The Lion King'....those powerhouse properties of the late 80s and 90s.
Most of the memorable classics up to that point had already been showcased in one form or another in the Park so their were not a lot of options left on the table.
There were very few appealing properties left by that point, but 'Song...' was one that held some real potential.
'Song of The South' experienced two theatrical re-releases in the 80s (1980 and 1986 ) so the film was fresh on everyone's minds...both at WED / WDI and the general public.
It was Tony who came up with the idea of combining the bright, colorful world portrayed in the animated segments with a flume Attraction that had been requested for development and needed to go into Disneyland's Critter Country.
He chose the film property for several reasons, foremost being the appealing characters, colorful setting, and memorable music.
It also fit thematically within the Attractions' intended location at Disneyland Park - right next door from New Orleans Square in a area that would become known as Critter Country because of it.
The Animatronic animal cast of the soon to be closed 'America Sings' Show was a happy coincidence, allowing Tony to save all of those figures from being lost which was a concern at the time.
So that was the second reason as to why - it fit thematically within the environment already present in that area of the Park.
Fun bonus fact -
The project had a personal connection as well, as Tony's mentor at Imagineering was the great Claude Coats.
Claude was the master background artist for the 'Song Of The South' animated feature, among many other Disney films.
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