Fair enough. This seems like an extremely (perhaps unearned) charitable interpretation, but if we assume the best, the “shared humanity” explanation works.Yes, but those are concepts in the film that would more accurately be described as prejudice or insensitivity. They insensitively make fun of American Indians (a cultural thing in Victorian era Britain; they were really fascinated with North American Indian tribes then), but there is no evidence the writers think American Indians are biologically or inherently inferior.
The lyrics don't claim their "moms" were ugly. It was a mother-in-law joke. Which leads us to...
The joke about the mother-in-law is actually an attempt to paint a sense of shared humanity with the Indians. The mother-in-law joke was a joke topic well used in the mid 20th century, often overused. It was a popular joke used on the Jungle Cruise about the elephants into the 1980's. By making a joke about Indian mothers-in-law, they are establishing that the Indians may have red skin but they are just like us.
I can post the lyrics again, but they're long.
The “fascination” Victorian society had with “native“ peoples is well-known. But it was, to use your preferred terms, a racially insensitive fascination. The issue becomes more complex when we consider how cultures changed between turn of the century UK, 1950s America, and today (the song obviously being a product of 1950s Disney/Hollywood).