It would be blasphemous and offensive to Japanese people to suggest these sites aren’t sacred. Yes, Japan is developed and people might not need to believe in the supernatural, but, to Asian people, Confucianism and respect for ancestors is borderline religion. The very word religion has different meaning in Asia, so to map it back into Western’s archetype of religion is weird. The word religion in the sinosphere could be translated as “way of living”, and tea practitioners consider their practice as such. Shinto, whether it’s actually belief in the Kami or reverence of the imperial family, is culturally the same. When American politicians float the word God, are they really speaking in actual terms or figures of speech?
Regarding the idea that Shinto is mostly a modern invention by the ruling class. The imperial shrines look this different. They have different motifs such as horses. Datapoint : I’ve been to thousands if not tens of thousands of shrines. The naming system of shrines is also a cue. It also doesn’t explain why there are thousand year old shrines, not in one region, but every region of Japan. Datapoint: I’ve been to all 47 prefectures.
Also, go to a rural remote fishing village. The shinto shrines there have a different level of spirituality. They aren’t tourist spots. They don’t have money. But the locals worship and pray for safe passage in the seas. When I went through Mie prefecture, the Ama, freediver women, have all had friends who died. The people in harsher economically deprived regions are much closer to reality, and if that’s not religion, I’m not sure what it is.