Not sure what to say. On one hand, I really liked the hummable tune and the characters of this ride. Splash Mountain tells a fun little story in a great way, with a musical score you're sure to be singing for the rest of the day or so. The characters are nice too, although I know them much better from the Disney comics than the movie (reading Disney comics is ... kind of a thing in Scandinavia, much like how speaking English is "kind of a thing" in the UK and US).
On the other hand, there's no denying it all ties back to a somewhat problematic movie. I haven't seen the movie myself, but from what I've heard it's not overly offensive in what it shows, but it kinda romanticizes "those good ol' days when we had good times on the plantations and the slaves had funny stories to tell". Not so much bad for what is shown, as it is bad for glorifying a setting and time period that was anything but glorious for those on the receiving end. And while Splash Mountain isn't overt in its references to its source material, the connection is well known. I can understand if Disney has been a little wary of keeping it around.
So, yeah, Splash Mountain was very fine in some ways, but it has some dark connotations that can't be addressed in a good way. Denying them doesn't work, the knowledge is out there. Acknowledging them only begs the question "then why are you still keeping it like that?" I think retiring it and re-thinking it is the best course of action. I have no doubt Disney could make an equally good ride experience even with a different theme.
Now for the big question: Do you think they will change its name? I don't think the name "Splash Mountain" ties into neither the movie nor its story in any way, so it should be fairly safe to keep it.