The dwarfy napettes in Ur-Fantasia do sound objectionable. Also somewhat objectionable is a stereotype that survived in film, the crows in "Dumbo".
But I don't find either Uncle Remus or Amos and Andy (the TV version) objectionable, and quite a few black people I've talked to don't either, because they didn't really demean those characters. Kingfish, Andy, Lightnin, & Co. were no smarter or dumber or more/less ridiculous than most white guys in TV comedies of the time. And Sapphire, Ruby, and Mama were all smarter than they, as SHOULD be in classic situation comedy.
Now, the radio version of A & A, with white folks playing black characters, is still funny but certainly doesn't cut it as acceptable these days.