We have people in this country who still pray to Zeus, not even mentioning the ones who practice witchcraft. The number of people who believe the Emperor is divine is small compared to the number of Japanese who are areligious.
If it were so, no jinja would be in operation.
Japanese media still is saturated with their mythology, whether it be yokai, oni, yoma or other monsters, including the divine personages that keep them in their place. They aren’t areligious socialists, as dangerous as that is in and of itself.