There is a long running video game series called assassin's creed that uses a concept of accessing genetic memories of an individual. A machine called the animus allows a person to relive the lives of their ancestors as if they were actually there. You would see the past through their eyes and thoughts. The purpose of this was to gain lost knowledge for historical reasons. Only certain people were shown to be capable of using this device.
Suppose humanity as a whole had the ability to access the genetic memories of their ancestors. This ability would be passed down from their mother, and would only contain memories of her direct ancestral line (mother, grandmother, great grandmother, etc). This ability could be used by anyone with a certain amount of training, but some would be more skilled than others. The further back the person lived, the more difficult it would be to access. This has led to the mainstream religion that revolves around honoring ancestors and an adherence to social tradition.
Given these changes to humanity, I would think that inheritance would be matrilineal and society would be broken up into clans. Mothers may be at the center of the household. A culture would develop in which ancestors are venerated and there would be strong emphasis on social tradition. "This has been the way it has always been done" would be common logic. Would this setup hinder progress and innovation in society? Will technological advancement suffer? How would it affect institutions like democracy?