Ah, I wish I was informed enough on that subject to give you a reliable answer.  I will be visiting my uncle next week, who is a graphic designer but has done a lot of thinking on this topic, what he thinks.

If you lined up models of building designs by Japanese architects alongside architects from Western -- monotheism-dominated -- cultures, I doubt very much I could pick out the Japanese designs.

I can say, however, that to my very unknowledgeable and superficial eye, Japanese cities are incredibly ugly and characterless, particularly in comparison to European and American ones.

We must remember that most Japanese cities were razed to the ground by ferocious U.S. firebombing during WW2.  However, Kyoto -- supposedly the mainstay of Japanese traditional architecture and culture in general -- was spared from the holocaust, and yet it, too -- in fact, it in particular -- is just ugly, almost depressing, in its banality and lack of imagination, lack of effort even, except as far as cleanliness, efficiency and safety go.

The most persuasive (even if not 100% convincing) explanation I have read is that the Japanese value the private, the inside, the small-scale far more than the public, the outside, the large-scale.  Thus, while private interiors, individual buildings, and smallest accessory can be utterly rich and beautiful, the overall assemblage of buildings, roads, bridges, train tracks, telephone poles, etc. on the town or city scale is just a mess, or a yawner, esthetically.

I have a couple of Western friends who claim they find Tokyo to be a beautiful city, but I think they mean beautiful "in a quirky way" or "from certain angles" or "at certain times of the day".

Oddly, though, I should admit that occasionally I stroll through some neighborhoods that I have been to in years, and while the first time I found them ugly or boring or characterless, the second time I say to myself, "My, what a lovely little neighborhood."  Is it that they have become "lovely" only in comparison to the even greater ugliness of the average neighborhood, or is that my subconsciousness has slowly started to become able to decode the esthetic language of Japanese "urban planning"?

As for Japanese "non-monotheistic" views about nature, I cannot think of a clear connection to architecture or urban planning in particular.  However, more generally speaking, I have noticed that what I read in books to be a certain "animism" that supposedly exists in Japanese culture does in fact exist: Japanese people have an astonishing sensitivity to cleanliness, order, form, and I believe part of this may come from a deepseated respect, even reverence, for almost any sort of object -- and its respective category -- you can think of.  So, everything is kept in good condition, everything is taken care of -- nurtured even -- almost as if it were a living being.  I remember, when I was about 7 or 8, I was rifling roughly through the pages of a book I was reading, and when my father (who is Japanese) saw these, he was a bit shocked and immediately explained to me, "Gently, gently!  You have to be nice with the book.  Books are nice (gentils).  They are so important and valuable.  You have to be nice to the book."  He wasn't talking about the monetary value of the book, which was almost nothing.  He was talking about books qua books, as well as about that book in particular, having a sort of inner value, even inner essence.  At the time, I thought my father was crazy, but I did as he said.  Only later did I connect his behavior with what I see now in how Japanese people handle things in general.

So, in the context of buildings and cities, the same applies: everything well taken care of, almost in perfect condition.  Everything is clean.  After a terrorism scare some years ago, perhaps the sarin gas attacks, the city of Tokyo got rid of public trash cans.  And yet, trash on the ground is seen rarely, or only at certain times of the day:  people feel "dirty" when they throw stuff on the ground; and the city itself makes it a priority to keep parks, trains and streets clean.  If a park gets dirty/polluted, not only will it be unpleasant for people, but the "God of Parks", and the "God of That Park In Particular", will be sad.

One caveat:  My mother's friend who in Tokyo in the late 60's for a year said that the city was a mess and stunk, chaotic, something like Shanghai or Beijing supposedly are today.  I have yet to hear someone else say that, but it could very well be true.  Even so, it might only have been a regrettable and exceptional but unavoidable phase in Japan's hyperaggressive industrialization, such as the episode of intense air pollution in the 60s and 70s.

Truth unfolds in time through a communal process.

There are some areas where Japan has been enlightened -- the age-old forestry regulations which probably saved it from becoming deforested like other island countries (Ireland & Iceland would have benefited from a few thousand Tokugawa bureaucrats) and some of the recycling programs a few high-tech companies have launched are pretty amazing, but specifically in cities, I defy you to find ANY examples of a particular Japanese concern for "equilibrium or balance between Nature and Man."

Just one example: up until World War II, Tokyo was famous for its waterways and canals. Now even the Sumida River is mostly paved over. And in terms of trees and park space, there is simply no comparison between Tokyo and, to take the example I'm most familiar with, New York. Central Park alone has almost 200 species of trees and a diversity of bird and small mammal species greater than the entire Kanto region.

If I were going to mount a "religious/non-religious" theory of environmental relations, Japanese agnosticism is not what would inspire me.