I don't see how this movie is racist.
True it makes a picturesque idyllic southern place and glosses over any racism that was rampant at the time.
But by that logic The Sound of Music (1965) must be racist because it does not mention the Nazism that ran rampant in Austria at the time. Oklahoma! (1955) must be racist because it does not mention the situation with the Native Americans in that state.
Basically any movie which portrays a place as idyllic without pointing out some flaw in the place must be bad. That includes any 60'ies show's like Leave It to Beaver (1957).
If it had portrayed black people in a stereotypical light or look down upon people because of the colour of their skin, it would be racist.
But the argument that this movie is racist boils down to "It's racist because it does not mention any racism". That's Like arguing that a recipe for lamb is really a recipe for fish because it does not mention fish.
It`s far easier to start a war than to end one.