In general, cult of personalities are clearly examples of secular religion although one that can become supernatural in the case of the Kim dynasty in North Korea.
Ceremonies and traditions that we continue because 'that is just how it has always been done'. There isn't some binary notion of you are religious or your rationalist, non religious people can hold non-rationalist thought.
Personally I don't really understand what you're on about with the scientific method, the parent didn't mention anything on it.