I think that's a inaccurate and misleading description. I think the correct term is "colorism" not "racism," and it sounds like those distinctions were more significant within the black community than outside of it. I don't think a stereotypical anti-black racist would accept a black person into a social club if his skin was as light as a paper bag.
https://en.wikipedia.org/wiki/Brown_Paper_Bag_Test:
> "The Brown Paper Bag Test" is a term in African-American oral history used to describe a colorist discriminatory practice within the African-American community in the 20th century, in which an individual's skin tone is compared to the color of a brown paper bag....
> The Brown Paper Bag Test was heavily documented and normalized with historically black fraternities and sororities (especially among sororities) and historically black social clubs founded before 1960, whose members selected others who resembled themselves, generally those reflecting partial European ancestry.[8][9] Some privileged multi-racial people of color who came from families freed before the American Civil War attempted to distinguish themselves from the mass of freedmen after the war, who appeared to be mostly of African descent and from less privileged families.