Gameable History: Domestic Polytheism

I'm listening to The Ancient City. Part 1 describes indo-greco-roman ancestor worship. It's a kind of domestic polytheism which I don't think I've seen represented in fantasy fiction (except, kind of, Mulan). 

To summarize the gameable bits:

• Each family has a god, and their shared god is the defining characteristic of a family.
• If funerary rites are observed, then you join with your god after death.
• If the god is kept satisfied (by feeding the sacred hearth, watering the family tomb with libations, and singing your family's hymns), then they offer protective blessings.
• The primary blessing is warding the land, but the family god can also provide a familiar spirit to protect family members on long journeys, help find good spouses, etc.
• If the god is neglected, their strength will diminish, and your ancestors will suffer and fragment into hungry wandering spirits.
• Gods cannot split or merge, and you can only worship one god.
• You can however switch to a different god via emancipation/adoption, or via marriage (which is a ritualistic form of emancipation from one family and adoption into another).
• The god legally owns the family land. It therefore can't be split or sold to a non-family-member. Primogeniture inheritance is less about land ownership and more about passing on a sacred priesthood.

Extensions

There's enough flexibility in the concept to accommodate magic systems with all sorts of implications. An idea not in the original beliefs but which I think would have fun story implications is if knowledge of the family hymns both grants greater access to and allows you to circumvent the protections of a family's god. True-name style tropes but for an entire clan. That would be a good seed for both inter- and intra- family conflict.

Curious Similarities

The book doesn't touch on this, but I've noticed that this kind of ancestor worship is fairly similar to some aspects of Chinese folk religion. I wonder if the similarities are coincidental, or if they're the result of cultural transmission, as happened with Greece, Italy, and India .

Or I guess another possibility is that neolithic peoples in multiple regions invented similar ancestor worship because ancestral spirits are actually real and all of my ancestors are starving because I've neglected the ancient rites. 

my bad if true 🤷