Religion
According to my brother (and my father) the Japanese no longer have any major religion. As a whole the culture is atheistic and materialistic. Note the definite lack of any religious reference in most anime. The few that do seem to include religion, such as Inuyasha, do it in some strange ways. Inuyasha has Monks and Priestesses, but they don't seem to believe in a higher power - not most of them. Instead, they believe in some vague concept of 'spirituality' which is basically just a way to explain why they have special abilities. They even say that one has "miko" blood, or "inherited" spiritual power from their parents. So it's more like a superior human race than actual religion. Plus, Kagome's grandfather is the only one who prays, and he is made to look like a well meaning, but powerless man. This also explains why there is a great deal of experimenting with sexuality, violence, and various degrees of reincarnation and sources of magic in Japanese entertainment. When you have no religion anything is fair game.
It is, however, interesting to note that in traditional Japanese religions (especially Shinto, which is the religion most commonly seen in historical anime - it involves mikos and priests, and an overabundance of small shrines) holy powers were thought to be passed down through the female line. For this reason religious families often took on the wife's family name rather than the husband's.