Earlier quoted context omitted.
You're not aware that Buddhism isn't native to Japan? And here I thought you were a cultural expert on all things Japanese. Although I did make an error - it's both Korean and Chinese.
its a japanese buddhist/shinto temple. an american church isn't roman. and buddhism isn't chinese.
So, yes, it's a Japanese Buddhist/Shinto temple. But the religion isn't originally Japanese, and neither is the architecture. The only thing native there is the Shinto.
No one considers modern Japan to not be Japanese, despite it being, in some sense, an American reboot of a Prussian remix of Imperial China. If you want to say Japanese culture predates the US by "thousands of years," fine - except you would need to ignore the thousands of years of European culture that America is based on to do so.
And also ignore the fact that, yes, modern Japanese culture is very much a product of the postwar period, making it both older than, and newer than, the US. And the aspects which are newer are likely the more relevant to Japanese people.