I would still say that is wrong.Sure, but saying that skin color isn't heavily linked to culture now is just wrong.
White people in New England don't share a whole lot in common with white people from Texas. And 'black culture's ignores the subgroups that have distinct cultures of their own.
A black person from a Jamaican background doesn't share a whole lot in common with a Somali refugee or immigrant, and both of those probably don't have a lot in common with a decendant of a slave living in Detroit.
And the various Asian cultures might punch you for putting them all under one banner.