I don’t think you would find a denomination with such a doctrine or statement, but AIG certainly is not shy about the association, as this excerpt from their book One Race, One Blood shows:
“Most people do not realize how intimately connected the popular idea of evolution and the worst racist ideology in history are. Ken Ham and Dr. Charles Ware reveal the compelling history of the effect of an evolution-based belief system on the history of the United States, including slavery, the Civil Rights Movement, and abortion.’
Of course, Ham does not say specifically that evolution is the sole cause, only that it is intimately connected. Ironically, listing slavery as an effect, when of course slavery predated evolution by a century or two in the Americas and Darwin’s family were staunch abolutionists at a time when Southern church denominations came into being because they supported slavery, and indeed many church leaders were slaveholders. Also ironic in that some of the schools that AIG promotes were the last holdouts in admitting black students, and later in banning interracial dating.
It is to his and AIGs credit that they no longer hold those views but the attempt at deflection is not a good look. And that quote strangely talks of the Civil Rights Movement as if it were a bad thing, rather than a reaction to a great evil. It was certainly a tumultuous time in the USA, but something that was necessary.
It is true that proponents of eugenics used Darwin’s theories as a measure of justification, but ironically also, they were looking to eugenics because they did not trust the evolutionary process and wanted to be their own intelligent designers.
Overall, while I do not agree totally with your position on original sin, I would wholehearted agree that the propensity to sin that seems ingrained within us has certainly manifested itself in these evils of individuals and society.
I think your observation regarding that the mark of Cain and later the curse of Ham were used by religious people to justify racism is true at one level, though ultimately other factors are also present.