Here is the problem with "Shinto" - and this may well be just my own perspective. So, take it for what its worth.
The term "Shinto", like it or not, is defined by history. That history includes deification of the Japanese imperial family who is said to be descended from Amaterasu, and is now soaked in the blood of an aggressive war that killed millions across Asia and the Pacific. Young Japanese threw themselves fanatically into war committing atrocities that the Japanese in general to this day still can't fully own up to.
Millions of Japanese, Chinese, Koreans, Vietnamese, Burmese, Phillipinos, Malaysians, etc. died in the name of the kami.
There is no way that is compatible with Nichiren's teachings.
The diversity of beliefs and practices you point to as proof that "Shinto" is not just State Shinto has a point. But, for the same reason the swastika is a symbol of hate rather than holiness for many people, "Shinto" is likewise stained with hate. Just look at people's reactions to Yasukuni Shrine.
But let's take this diversity of beliefs and cults that also goes by the label "Shinto" - is it really compatible with what Nichiren taught? I don't think so.
Shinto literally means, "path of the gods".
The Great Vehicle does not ride on the path of the gods.
The term Shinto implies the superiority of this path of the gods over all other paths. To say that one is following shinto - one is following the path of the gods. That cannot be reconciled with NMRK.
What we have now that is called "Shinto" is a self conscious separation and constructed idea of kami reverence that emerged long after Nichiren was around. The tension between the various kami cults and Buddhism has been there from the beginning when Buddhism was introduced from Paekche. Shotoku Taishi's political victory and the Imperial family's subsequent devotion to Buddhism for centuries after placed Buddhism in the supreme position. Nichiren lived at a time when Buddhism was the view. it was conventional wisdom that Buddhism is the ultimate truth and kami, to the extent they had been converted into protectors, were part of the Buddhist pantheon of helpful and protective spirits along with Brahma and Shakra, and the hosts of dharma protectors who came from abroad. This view underlies Nichiren's criticism in Rissho Ankoku Ron - the kami, and the rest of the Dharma Protectors, he argued, had stopped protecting Japan because the people had turned into slanderers of the Sublime Dharma.
While some of those kami cults that are called "Shinto" now were around then and have continued uninterrupted to the present, historically they were closely related to Buddhism. It was only in the late medieval period that there was movement to distinguish themselves from the Buddhist view.
Buddhism finally fell as the predominant view following centuries of corruption in the Buddhist institutions, punctuated by the destruction of the Tendai monastic complex at Hiei-zan by Oda Nobunaga. In the centuries that followed him, the Edo or Tokugawa period, Buddhism was neutered and when Japan was threatened from the outside, the people behind the Meiji restoration drew on the putative nationalism in the Imperial kami cults to complete their authority. All those other kami cults you guys point to as "not State Shinto" all ride the wake of Imperial Shinto for their character as distinct, native spiritual traditions. The odd exception that lets foreigners participate does not change the basic underlying consciousness that they are about nativist identity. (I guarantee that as Japan accepts ever greater numbers of foreign workers, we will see some strain of nationalistic Shinto rise up as a reaction. The elements are already around.)
When I go to places like Meiji Jingu, I'm taken aback by the expressions of reverence by Japanese because of its nationalistic meaning, and ironically bemused by foreigners offering prayers. I don't get the same feeling when I encounter a little old lady making offerings at a shrine to a tree sprite up in the mountains, and while it would surprise me to see a foreigner do that, it would not strike me as ironic - "Oh, you get it about the tree?"
Back to Nichiren - the various Shinto cults around now imply a view about the supremacy of the kami path - this is not compatible with Nichiren's teaching that Buddhism, and the Sublime Dharma in particular, is the supreme path. Nichiren taught NMRK. All else is extraneous. So long as what you otherwise do does not conflict with NMRK, no problem. Nichiren himself fully acknowledged and engaged kami. But he did not follow shinto.
Utsubusa came a long distance to visit me despite her advanced age, but since I was told that it was merely a casual visit on her way back from the shrine to the god of her ancestors, I would not see her, although I pitied her greatly. Had I permitted her to see me, I would have been allowing her to commit slander against the Lotus Sutra. The reason is that all gods are subjects, and the Lotus Sutra is their lord. It is against even the code of society to visit one’s lord on the way back from calling on one of his subjects. Moreover, Utsubusa is a lay nun and should have the Buddha foremost in mind. Because she made this and other mistakes as well, I refused to see her.
Letter to Misawa