That was never the intention when they built Splash Mountain. If Disney were really supporting and commercializing the film, they'd have released it on DVD multiple times and sold merchandise of the film's live action characters.
Hasn't hurt Dumbo the Flying Elephant. Or Peter Pan's Flight. Or Mickey's Philharmagic, which has elements from Fantasia in it. Or The Magic Carpets of Aladdin or the multiple Little Mermaid and Lion King rides, even though I've heard people claim those films are racist. It doesn't seem to have hurt the retheme, either, despite the fact that there are folks who think The Princess and the Frog is racist.
Heck, the fact that Mickey and Goofy have starred in shorts with racist stuff in them hasn't hurt Mickey's Runaway Railway, or the entirety of Mickey's Toontown. This whole mess got started because Song of the South is an easy target.
I'm not defending Song of the South, but this isn't about Song of the South. This is about Splash Mountain.