I'm not sure that I understand the question. Strictly speaking blood does not actually have anything to do genetic inheritance.

From a scientific point of view blood types are the result of genetic inheritance, not the mechanism. In fact if you are trying to check for DNA it is usually taken from epithelial cells because red blood cells have no DNA. DNA and blood types are from the 20th century.

From a cultural point of view there are very old metaphorical connections of blood both to life and to kinship. The life aspect is obvious to any culture that eats meat. The kinship angle is also very old, the Romans using the term "consanguinitas" the way we use the term "blood relation". In Islam it was said that human life begins as a clot of blood in your mother's womb. I would love to hear more from someone who has studied why kinship is identified with blood.

So I'm a little confused on how to answer the relationship between the two.