Completely being discrete doesn't define what is a "culture." Cultures are aggregative and not taxonomical that way.
For example Anglo-Saxon culture is distinct from the Saxon, Angle, and Jute cultures that came before. It is distinct and worthy of study on its own, but is different enough to be a separate area of study.
Same with the way Haitian culture is distinct but still a descendent of the Dahomean culture that came before and has elements of French culture.
I could see a number of academic approaches that would fill dissertations and journals arguing back-and-forth as to how much "human" culture is still present in "mutant" culture 100 years in the in-story future.
Entire tenures and careers would be built on the vagueness and disagreements over those sorts of points... just like people who still argue over how much Indo-European culture influenced the natives in India and created the Vedic culture.