On New Year most Japanese visit a shrine, but it does not mean they are believe in the traditional Japanese religion, Shinto, while it is said that over 90% of the Japanese belong to Buddhist faith, but it is only as a matter of form. They do not have the custom of daily worship. They visit only at funeral.
Ironically, they celebrate Christmas without hesitation. Moreover, most Japanese hold their wedding ceremony in church. You may say religion is used mostly as their event.
On the other hand, Japanese feel free to criticize politics. No one would be condemned for criticizing politicians, even the Prime Minister. However, Emperor is exceptional. He is the symbol the Japanese, though he js not involved in politics.