I've lived seven years in Japan. Even if I were to get Japanese citizenship, I wouldn't identify myself culturally as Japanese (and neither would Japanese think of me as Japanese).
Countries like the US separate cultural identity and citizenship, so having citizenship but still being seen as a foreigner might seem a bit strange at first. On the other hand, if I was to go to the US, there are certain cultural identities I could never have. For instance, as a white guy, I could never be treated as an African American, no matter how much I wanted to be or tried.
This hasn't stopped a great many white guys from trying!
Yes. It's very different to what you get, for example, in Australia. Or most parts of Europe. Yes, you'll probably be a gaijin forever, even if you get naturalized (and renounce to your other nationality). But there's a huge difference between what the japanese are, and have always been, and xenophobia. Of course you get a different treatment unless you show them what you know and your respect, but it boils down to the kind of society it is and the fact that you're, at first sight, different from them. But different, not worse.
The US is occupied by an enemy force that they supported and elected. Every time another basic human right is violated by the legislative and executive branch those cheer. Does it matter that drunk driving kills more people per year in the US than acts of terror? Does it matter that more people die from prescription drug dispensation mistakes? Not to the mind of the scared American.