Thank you for replying. I found your lists of some of Hardings ancestors to be interesting. I am recalling from memory the exact words of the author (the book is in storage and buried in a box.) Some of Harding's family relations appeared to be murky. I think there as a case of not to much known about them or there ethnicity was not established and it was in a way that was very mysterious to the author who was a leading scholar of American First Ladies. Any black ancestry I think was not from the Mayflower obviously. But it was apparent that Harding was considered black by many people in Marion including his own Step father who actually campaigned against him on that ground. The step father later accepted the marriage and was quoted as saying that Harding was the "smartest nigger I have ever known" (his language not mine). I don't know actually what the truth is about Harding's lineage but I suspect his own stepfather would have known the truth.
It could be the stepfather was just an early-20th century KKK-wing Democrat. :')
My own ancestry is a mystery past about four generations -- iow, I know some of my ancestral lines (assuming the records which exist tell the whole story, which they obviously may not) back to the 16th century, and they're all commoners, every one. But some of the lines (particularly of my female ancestors) just drop. Obviously there was someone there, but their identity is no longer recorded AFAIK. My most recent German lines only go back three generations. :')
Tracing the ancestors eventually becomes a looking-for-images-in-the-clouds activity, unless one is careful. One 19th century professional genealogist knew what sold, and made up a medieval French king, and just kept sticking him into the family trees of his customers. He must have had a booming business. ;')
Analogously, there were at least two otherwise unrelated families fighting over who was really the descendant of Jesse James. (':