Disagree, there is absolutely no insulting of black people in that entire film. There's no slander, there's no disrespect of black characters (certainly not based on their race) and Uncle Remus is clearly intended to be the films 'hero'.
People only claim it's racist because it is set shortly after the abolition of slavery and features a black man living around a plantation. So it makes people uncomfortable, but it's probably an accurate situation considering he's an old dude who I imagine didn't have anywhere he could go at that point in his life. And even if he was bitter about white people I doubt he would take it out on the kids, which it seems is what people wanted to see in a CHILDREN'S FILM.
Regardless, it's pretty irrelevant as Splash Mountain has almost no references to the film outside of the cartoon portions.