Phillip DeLoria's book "Playing Indian" discusses the various historical instances of we Europeans making assumptions about the "red man". The racism in the song is part of the idea, prominent in the Eastern part of the USA around the 1840's, that The "nobel red man" had vanished. It was a convient myth. Clubs of European-Americans mimicked what they knew of Native American culture, including the fabrication of Indian artifakes, done as close to the "real thing" as possible. They performed "rituals", they adopted Indian "names". They considered the Indian to be "Quaint", exotic, and non existant (In their experience he was). Abolishionists were notably quiet about the wrongs done to the American Indian. It was not fashionable.
The only positive thing to come from this view of the "Vanishing American" was that some of those members of the "redman" clubs were darn good at creating Artifakes to the point that some collections today have numerous items made by people as far removed from being Native American as imagineable.
Or so I've been told.
A bit of irony: Crazy Crow Trading Company, of Potsboro, Texas, the biggest supplier of materials for making Indian artifakes is owned by a family with close ties to the Comanche Nation.