One of the issues that the Shinto establishment has a strong opinion on is the revision of the Japanese constitution. They believe that it should be revised, as soon as possible, and are very actively engaged in campaigns to bring about that change.
To understand their position, a bit of background on the current Japanese constitution is important. It was written, in English, by a handful of Americans over the course of a few days, translated into Japanese, and then passed by the Diet in accordance with instructions from the occupying US forces. In later interviews, the people who drafted the constitution have said that they expected it to be heavily revised, or completely replaced, almost immediately after the end of the occupation.
However, the US military attorneys who wrote the constitution did a very good job, and did pay attention to Japanese history and concerns. The result was a constitution that most people thought was generally pretty good, and that few politicians saw a burning need to change. As a result, it has never been amended.
The first, and possibly most fundamental, argument that the Shinto establishment makes is that Japan should have a constitution that was written by Japanese people, in Japanese. While it is hard to argue with this in principle, we can only amend the constitution if we actually change it, so they also have specific proposals. These are more controversial.
The most controversial is that they want to change Article 9, which renounces war as an instrument of national policy. The most recent proposal from the head of the organisation of Diet Members affiliated with the Shinto establishment (who also happens to be Prime Minister Shinzo Abe) is to add a third clause to the article saying that Japan can have Self Defence Forces. This is very controversial on a national level, and controversial within the Shinto establishment, but for different reasons. It is controversial on a national level because many Japanese are very reluctant to touch Article 9 at all. It is controversial within the Shinto establishment because he plans to leave the renunciation of war untouched, and won’t even call the military forces the “National Defence Army”.
A reasonable analogy for the political position of Article 9 would be the Second Amendment to the US Constitution. It generates a lot of controversy, and the Japanese Communist Party (which has a significant number of Diet members) runs campaigns to preserve Article 9. Supporting modifications here means taking a definite stance on a divisive issue.
Why are the Shinto establishment so keen to have an army? I am, honestly, not entirely sure. There is a definite militaristic tone to the Shinto establishment that is not supported by anything they say officially about what they believe.
The other changes they want also tend to mark them as right wing, but make much more sense given their position.
First, they want the preamble to be rewritten to reflect Japanese history and values. The current preamble is basically “we promise never to wage war ever again; please don’t hurt us”, so there is room for revision. (And, it should be noted, we have kept that promise.) It makes sense for Shinto organisation to want the preamble to reflect Shinto values, although that would require agreement on what Shinto values actually are, so there may be very good reasons why I have never seen a concrete proposal.
Second, they want to change the clauses governing the Tennō to make him explicitly the head of state. The current constitution makes him a symbol of the Japanese state and people, and requires that he both sign all laws before they come into force and appoint the Prime Minister and other ministers, so the Tennō is treated, internationally, as the head of state of Japan. However, the constitution does not specify that, and the Shinto establishment would like it to. Given the central role that the Tennō plays in their conception of Shinto, as discussed in one of my Patreon essays, this is not surprising. (Incidentally, the constitution requires the Tennō to sign the laws and appoint the ministers that Diet presents him with; he has no choice in the matter.)
Third, they want to change the clause separating the state and religion, so that the state can participate in and support Shinto rituals. Shinto has, historically, been very closely linked to the state, and so this is also unsurprising. I think this has no chance at all of being passed in the foreseeable future, but it is hard to criticise them for wanting this.
Fourth, they have recently started talking about a “family clause”, supporting the “traditional family”, by which they mean the imitation of the Western family structure that was imported to Japan in the late nineteenth century. (Many of the features they mention were not features of Japanese families earlier in history.)
Finally, they would like to change the constitution to make revision easier. This arises from frustration with how difficult it has been to get any amendments, and is understandable, but has nothing to do with Shinto as such.
Some people suspect that the Shinto establishment would like to restore the Meiji Constitution, in which sovereignty rests with the Tennō. I do not believe that to be the case. They do occasionally argue that the Meiji Constitution was not as bad as all that, and they are right; for a late nineteenth century constitution, it is actually quite liberal, and it did establish a basically functional democracy, and lay the foundations for the post-war order. However, it is wildly unsuited to the present situation, and the Shinto establishment seems to be well aware of that.
Constitutional revision is basically a right-wing position in Japan, no matter what the content of the proposed revision may be, and the revision of Article 9 is strongly associated with the hard right, denial of Japan’s war guilt, and a hankering for military adventurism. It is hardly surprising that this draws criticism from substantial sections of society.