You've inadvertently described the US. A lot of our culture and traditions are a mismash of the immigrants who came before.
As for Japan being "pure" culturally, that's a fantasy conjured up by "nationalists" if you're generous or xenophobic racists when we're not.
The historical lineage of the Japanese includes continuous mixing with the Chinese and Koreans, alongside the Ainu and Ryukyuan. Elements considered central to traditional Japanese life were borrowed from neighboring civilizations like China, with Buddhism and rice cultivation being the most well known. I'm sure there are plenty of other examples, and we haven't even gotten to the modern era.