Disclaimer: I'm an African american.
Not saying it is applicable today but let me give you another point of view.
First, that terrible time in history is not really history. we are not talking 1 generation yet. I'm a disser and when I was a little girl, in order to visit my grandparents in Knoxville tenns from nyc. When we got to Washington dc, I had to get off the train and go to the "colored" section on amtrack because the south was segregated. So try to remember, this 1 drop rule is not some ancient history.
Next, like most oppressed people we took the oppression and tried to fashion a culture around it. the one drop rule was often a way for our light skinned brothers and sisters to claim an heritage that the outside world was constantly saying we were "less then". When I was a kid "biracial" was a not a "good" thing. 9/10 times you were ostracized by white folks so the 1 drop gave you kinship to peoples who would accept you for "belonging" to them.
Lastly,
Yes we embrace our history. we are a people who have had to fight for every single "right" that caucasians were granted simply by being born. From George Washington fighting a war of independance all the while routinely sending slaves back to virginia so as to not have to free them until today. We have fought, died and sacrifice for a country that has never ever treated us as one of its citizens. Yet we survive and continue to contribute to that very same country.
My dad a Korean and vietnam vet who won medals and accolades for a country in which he could not even see a movie in his home town because he was colored, still served his country. So yes, I embrace that horrible time in history because we over came it.