In Japan, most people die Buddhist. (Born Shinto, Marry Christian, Die Buddhist) However, a few people do have Shinto funerals, and some family graves are Shinto graves. (Cultural difference alert: Traditionally, people in Japan are buried in the family grave, and the grave stone just says that it is the family grave. The individuals in the grave are recorded somewhere, but that seems to vary.) Traditionally, members of the family tend the family grave over the generations, and perform the appropriate rites for their ancestors. There are even special provisions in tax and inheritance law for what happens to the ownership of the grave (it is not taxable, which if your family grave happens to be in central Tokyo may well be a very good thing).
However, this system is breaking down. People do not stay in the areas where their family lived, and a lot of people have no children, so there is no-one to look after the graves. As a result, there is a move towards customs in which a religious professional takes over the task of making sure that your ancestors (or you) get the appropriate rites in perpetuity. We get leaflets about the Buddhist version delivered to our flat fairly often, because the complex was built in the 1970s and now has a lot of elderly residents. (The Residents’ Association has to keep raising the age at which you get a gift on Respect for the Aged Day.)
The November 18th issue of Jinja Shinpō carried an article about a study meeting in Ibaraki Prefecture at which priests discussed the issue.
The standard Shinto approach appears to be to establish a “soreisha” (祖霊社) in the jinja precincts. A soreisha is, literally, an “ancestral spirit shrine”. It is not a graveyard, but rather a place where matsuri can be performed to honour the dead who are enshrined there. Traditionally, a Shinto family has its own, kept in the house below and to one side of the kamidana, but that has never been terribly common. (Most families honour their ancestors at the household Buddhist altar.)
The discussion was mainly about the practicalities. To establish a new soreisha at a jinja, you need three things: land, money, and permission from Jinja Honchō. One priest, who works at the prefectural Jinjachō, gave a presentation that was, apparently, almost entirely about that last point. I hope that he was explaining that it is not as complicated as one might think, but that is only a hope. Another talked about the process of buying more land and paying for the structure, getting permission from Jinja Honchō, and now applying for permission from the prefectural governor. That last is necessary because changes to the regulations of religious corporations need to be approved by the prefectural governor, although I believe it is generally a formality, as the constitutional protection of freedom of religion puts severe limits on how much they can interfere.
In the open discussion, people asked about the upkeep of soreisha, and how long after death the spirits of the dead should be enshrined in them. There were not, it seems, any questions about the appropriate matsuri, because those are all well established.
This is an example of an adaptation to changes in society that is theologically easy, but has practical difficulties. Alas, not all the problems are like that.