When it comes to the Nippon Kaigi, of which many LDP members are also a part, State Shinto is a component of their ideology, so it is a religious right in a certain way.
True, there's a weird cultish aspect to it, but it's more connected to the nationalism than it is scripture dictating social issues, like we see in the west.
Japan has its own alt-right, who are anxiously waiting for Abe to bring back a strong Japanese military.
The thing is, war is so far removed from Japanese life that no one here knows what it's like anymore. Japanese media and education shies away from it because they think it's too extreme to show.
No one's lost a family member in a war, no one has a family member dealing with ptsd, so on. They just wanna see Japan push back against China and Korea, they don't actually know what they're getting into.