It will perhaps surprise very few that my reaction was -- the ancestral cults of ancient Rome and China! Devoid of all four elements. The Chinese books that describe it are like etiquette books, after the fact codifications, and advice to keeping up to snuff. I'm not sure that Romans had even that. And prophets, cult leaders, and priests are right out. But it's still a religious practice.
And there was the time when someone was asking for advice about a priesthood, and I pointed out that becoming a priest was not necessarily a matter of deciding to take the job. Many cultures had hereditary priesthoods. Or -- in ancient Rome the pontifex, include the pontifex maximus, was an office. Julius Caesar held it. And they were elected. And they needed to be married because they could not preside over the rituals of Bona Dea so their wives had to. IIRC, they also had to have children, but in case of childlessness, could select a boy and a girl from other families to carry out the proper rites that could only be conducted by children. (Though that may have been a Greek priest that I am thinking of.)
Research -- it's not only good for answering questions, it's good for inspiring them.