People who object to these songs and stories have no conception of history and how the past shapes the present and our response to it.
Piccaninny is not Victorian; it saw print at least as early as 1657, when it was used in the Barbados, by Negros, for a very small child. The word comes from the completely acceptable (I hope) Spanish pequeniño, or wee child (OED). Spanish remained common in the Caribbean islands and region for years after the British takeover. The word came to the Louisiana area with Spanish planters and with slaves transferred from Caribbean plantations to the mainland. Introduced to Australia, South Africa and other areas, it was "commonly used by the natives themselves." Certainly it was the usual term among southern Negroes, slave or free, for their wee ones.
The word is also related to the American picayune, or very small, from the Sp. half-reale, a coin still in circulation in the States until the mid-19C. (Harriet Beecher Stowe, in Uncle Tom's Cabin).
Limiting consideration of these terms to southern cultural propaganda also betrays ignorance; slavery was not legally proscribed by the British until 1833, but continued covertly in the Caribbean, and particularly in the Australasian area, until after the time of the Emancipation Proclamation.
I also suggest, for the general Anglo-Saxon British views, the Encyclopaedia Britanica 11th Edition, post-Victorian, be consulted.