I am a scholar of International and Japanese Studies of the University of Tokyo, and I'll be happy to give your question a shot.

There are a few misconceptions about Japan I need to clear up first. The first is the urbanisation of Japan, which you briefly mentioned. Japan has had dense city populations for a fairly long time in Edo / Tokyo especially (it may have been spurred due to the "Alternative Attendance" (aka. Sankin-Kotai) system of the Tokugawa Shogunate), but it's a misconception to interpret this as "dense urbanisation". Matter of fact, it was not until 2011 when 50% of Japan's population officially lived in cities proper. Japan has been, and still is, a very rural society outside of the "Pacific Belt" and Sapporo. Another important thing to keep in mind is that although the city populations were not extremely small, before the Meiji Restoration and in the feudal era, those who lived in cities would have been the members of the court, those directly under them, the families of Daimyo, some Daimyo very loyal to the Shogun and a few others (such as merchants or artisans, or peasant children who came to work for Daimyo). The standard layman would not live in Edo, Kyoto, Osaka, etc, and if you were to pick a Japanese person at random, chances are they would not have lived in a city.

Secondly, Shintoism. Shinto is regarded by many scholars, including myself, as more of a propaganda tool than an actual religion. Of course, it is an ages old native religion of Japan, but the part which is not so often mentioned is the fact that before the Meiji Restoration, Shintoism was essentially seen as an "old / has-been" religion. It was rare for people to really believe in it, and temples and shrines were essentially fused (which is why even today you can pray at Japanese temples, despite Buddhism not really having a deity to pray to). The Meiji Restoration massively upturned Japanese society and established Shintoism as the state religion, in what is often termed "State Shintoism". This was not a "return to our native heritage" movement, this was deliberately a move to reorganise Japanese social structure from a hierarchical feudal system into a patriarchal system with the emperor at its head, and in turn, complete loyalty to him. Before this point, emperors weren't really known or respected, and many of the "traditional Shinto" ceremonies are completely invented (eg. The Shinto marriage ceremony is a 19th century fabrication, as are most of the ceremonies performed by the Emperor today). Some would claim Shintoism was so strongly advocated so as to repel the influence of Christianity in Japan after the abrupt end of sakoku. I don't want to go in to too much detail here, but the point is that until the Meiji Restoration, Shintoism was not a major part of Japanese society or people's lives. Even during the Second World War, Japanese POWs would describe themselves as Buddhist, rarely Shinto.

One important point is that Shintoism emphasises that kami are borne of natural environments, which is why major shrines such as Meiji Jingu and Hokkaido Jingu are surrounded by lots of untended forest and vegetation that you're not allowed to enter into. What should be known though is that most shrines were built after the Meiji Restoration, so the usefulness of analysing the Japanese relationship with nature before 1868 through them is limited. This belief and the belief in Kami being everywhere was not entirely abandoned, though, and did cause the Japanese to respect nature slightly more than Western societies, however, it was not only Shintoism that did this. Buddhism also emphasises respect for living things, plants and animals alike, and would have influenced this view. If Shintoism had any effect on the Japanese attitude towards nature, it would have been before and perhaps for a century or two after the 6th Century when Prince Shotoku introduced Buddhism and the Seventeen Point Constitution.

I think alternative reasons as to why Japan is more covered in forest than other developed countries should be analysed in order to pin the exact significance of Shintoism.

One of those alternative reasons why a lot of Japan is very forested is simply because it's difficult to establish settlements in most of the country's land. It's mostly mountain, with larger cities being established on the plains and countryside scattered in between mountains. People don't really like building up steep hills, so the sides and tops of mountains are largely untouched. This isn't really related to Shinto.

Japan also encompasses Hokkaido, which is extremely unpopulated to another level, with the exception of Sapporo. Hokkaido is massive but holds about 5% of Japan's population. The Ainu, who inhabited Hokkaido before the Japanese, were hunter-gatherers, so it goes without saying that they didn't care much for destroying the land that sustained them. While Japan did colonise Ezochi during and after Meiji, making it Hokkaido, it is still by far the most natural area of Japan, which would massively rise the forest cover of Japan's land. Again, this isn't really to do with Shinto.

However, after the Meiji Restoration, Shintoism undoubtedly had a place, and to this day, even they don't necessarily believe in it, Japanese people will follow Shinto traditions and ceremonies. Even if these are invented by Meiji, it's still extremely significant in the Japanese way of life. Therefore, it is fairly likely that the Shinto influence has guided Japan's policies towards nature since then. For example, the drive for Japanese nuclear power was backed by a desire to drive down the consumption of fossil fuels, and this was only rolled back after the Fukushima disaster. Even after the Fukushima disaster however, there was a national drive (with the slogan of 頑張れ日本！) to consume less energy while the country figured out what to do next, which is both evidence of this familial national structure build by Shintoism and also a respect for the environment. Your reference to Japan leading environmental issues in the modern world may also be evidence of this.

In conclusion, I think it's reasonable to say that prior to Meiji, Shintoism was of negligible influence. If any religion did have an influence, it was Buddhism. However, after Meiji, Shintoism was driven into the very heart of Japanese society, which undoubtedly affected the national psyche and outlook of Japan, and therefore, would have had a fairly considerable impact.

I hope this helps!

I appreciate u/IceWizardz 's response, specifically regarding the urbanization and geography of Japan. However, and no disrespect intended, I find the analysis of Shinto somewhat lacking. Shinto did not disappear (not even culturally) with the rise of Buddhism, and then suddenly pop back into existence by declaration of Emperor Meiji. Instead, Buddhism and Shinto have shared a deeply interwoven history for well over a millennia and a half. The primary issue is, as someone else mentioned, the fact that for quite some time, there just wasn't a proper name to pin it with. Additionally, there is nothing in the nature of Shinto as a proselytizing belief system, whereas the spread of Buddhism was backed by considerable resources and personages throughout Japanese history. While this may lead one to assume that Shinto is a "weaker" belief or influence on society, all it really shows is that Buddhism enjoyed centuries of a certain cultural spotlight. More specific cultural practices of the time such as bushido, the tea ceremony, etc. also draw far more blatantly from Buddhist influence, though none are completely without Shinto.

Diving deeper into the history of Shinto, we find that the Meiji restoration was a complex time. While the establishment of government-mandated Shrine Shinto and near-hostility to Buddhism, which quickly paved the way for State Shinto, was a clearly authoritarian ploy to wrest power in the name of the Emperor, this is not the only consequence of the time. Shinto was never a "has-been" religion; rather, there have been multiple occurrences throughout history where it was nearly swallowed whole by Buddhism. The cultural relevance never faded, but the theological elements - that is, the nature of kami, and their greater significance in the world - varied wildly throughout history. To put it mildly, a millennium of alternating religious syncretism and subjugation was more than enough to fuel a desire for change within the Shinto clergy, and the Meiji Revolution's emphasis on the reinvention of Japan on the international stage gave Shinto the catalyst it needed to attempt to reforge its own identity independent of Buddhism. On top of the Jinja Shinto which led to Kokka Shinto, the Meiji era also saw the formal codification of the thirteen Kyoha Shinto branches, the state ideal of Shinto as a national philosophy, the massively increased religious regard for the Emperor, and, overall, the birth of a new national identity, all of which contribute to the idea of Shinto as a new construction. So while understandable, portraying Shinto as wholly or even mostly birthed in the late 19th century is untrue.

There is also the difficulty that Shinto is more than just a collection of kami and shrines, but rather a full belief system, philosophy, and way of life, as indicated by the 道 (michi/do: way, path, course) character in Shinto 神道. It is different from the way one might define themselves as Christian or Buddhist, but rather an integral part of the Japanese identity, named or not. There has been ongoing controversy for years now whether the definition of religion in Japan as it currently stands (宗教 shuukyou, literally "religious doctrine") even applies to Shinto, a religion with no organized doctrine or dogma, yet which still retains certain concrete beliefs (the existence of kami, the importance of purity/purification, a respect for one's environment, and so on). The reason people familiar with Shinto don't refer to it as an "ism" is precisely this: there is no teaching to follow that could denote it as an "ism." 

Thus enters the difficulty with defining how Shinto specifically affects environmentalism in Japan. It's undeniable that reverence for the world we live in is has contributed to Japan's environmentalist efforts. The notion of kami in all things gives Japanese culture a natural respect for one's surroundings. I think it's safe to say that just about all environmental efforts from Japan, even from ancient and medieval times, have been strongly influenced by Shinto, though in more modern times (from the Meiji revolution and onwards) moreso brought on by the international community - first by a desire to be recognized by it, and now from a desire to remain at the head of it. However, I doubt, unfortunately, that there is any quantitative way to see specifically just how much of an effect there's been. 

Interestingly (and without passing judgement), Shinto as a political device today has been far more taken by conservative elements, primarily in relation to Kokka Shinto and far less so in relation to any environmental points. So take what you will from that. I hope this all helps to add a different note to your analysis!