Shintoism and Buddhism aren't mutually exclusive. In fact, the two religions are fused in a rather unique way in Japan (cf. https://en.wikipedia.org/wiki/Shinbutsu-sh%C5%ABg%C5%8D ).
Both religions lost its belief system today and there are only a set of practices, so many people do both. In this sense, they aren't really "religions" in the Western sense.
Buddhism was extremely popular and influential in Japan until roughly the time of the Samurai, though many factors are involved with this change. It is interesting that in Buddhist dominated Japan use of cannabis was common, even ubiquitous. This changed completely with the rise of the Samurai, leading to the strongly anti cannabis and alcohol tolerant society in Japan now.
I was under the impression that Japan's anti-cannabis culture came about as a result of American occupation and postwar industrialization (the latter, primarily, to favor synthetic rope and fabric manufacturing over Japan's native hemp industries.)
Japan is more of a syncretic society than any one or another thing. I believe a popular saying over there is something like "Born Shinto, marry Christian, die Buddhist."
