Before going to Japan I was worried about the same thing, too. But one of my professors told me that although they're everywhere, it's more the Japanese who keep to themselves and do stuff like post on 4chan who are the really xenophobic ones. I found this to be pretty true during my stay there, although I admit, of course, this is only anecdotal.
In Japan, I didn't meet any overt racism, but that doesn't mean it doesn't exist. Your ethnically Chinese friend living in Japan is proof of this. Take whatever incidents may come your way, but also remember that it won't represent the whole of Japan. Do your best to meet and reach out to as many people as possible both inside and outside work, and you'll see.
Yes, the friction between Japan and China is a huge sticking point, but that's just one side of a multifaceted issue. Today there are more and more Japanese students going to China, and other parts of Asia, to study abroad. Japanese businesses are obviously more eager to do transactions with China. In general, China's rise hasn't gone unnoticed by Japan. That doesn't mean all is fine and you'll be treated like a king, though, but it does mean that Japan is not that hostile to China/Chinese.
My advice to you is simple: go do JET, or if you can't do that, do eikaiwa. Show them that you're willing to be a positive role in their community. You will probably feel a pang of jealousy of the different way people treat you vs. other foreigners, but that just means you gotta keep trying harder and smarter to make your mark. Your Mileage May Vary, true, but remember you also have control of what you can do. Don't forget, you're gonna be in JET as a cultural ambassador, and if this issue bothers you, do something about it in a productive and positive way (i.e. no screaming at random passersby to stop being racist
Ultimately, you don't want to be accepted for what
you are, you want to be accepted for who
you are, and what you do
Also…. don't do dances for idiots. You're nobody's monkey.
Please let me know here or by PM if you have any more questions! I'd be happy to answer them.
(Incidentally, the non-tourist Chinese people I've met in Japan have been very kind. They might even approach you and you can have a chat with them in some instances when they find out you're not Japanese