However. . . .
That doesn't mean that the rites will be organized the same in every culture. In particular, it doesn't mean you can look around, scrub off the serial numbers, and use modern day religious practices in your new culture.
Some cultures will bar characters from rites on grounds of class, or martial status, or what have you -- in ancient Rome, some religious rites had to be performed by univiri, or women who had had only one husband, and many rites were either patrician or plebeian.
Plus, of course, you had different interests. In polytheism, that will naturally send people to different altars. A character won't actually want to offend any given god, but he's likely to stick to those whose good will he most needs. Things of city, or region, wide importance, like agriculture or fertility, may have annual festivities, but attendance may not be mandatory. And it would be very odd indeed to regard one of them as primary in a polytheistic culture -- all the gods (by definition) have their place. Mystery rites and other such specialized cults are even less central and more likely to be individual.
Familial rites may be some form of mandatory. Someone has to keep the ancestral ghosts content and from roaming about dangerously. Or the household gods. Similarly, the state's chief interest in religion is often ensuring that no one is ticking off the gods, and they are receiving their proper propitiation. Seriously, this gets enormously underplayed in many allegedly polytheistic, pagan settings. Gods are by definition not good people to tick off. The Roman legions had a long list of sacrifices that each legion had to make, and only then could they add their own personal religious practices for whatever gods they wish to propitiate.
And really beware of weekly worship. It wasn't common. Some early Christian martyrs were caught because they were seen congregating on Sunday where they couldn't have been going to work, and so obviously it was religious -- and who had religious practices on Sunday?