Actually many non-Japanese have Japanese citizenship, are protected, permanent residents, and can vote.
Like in many countries, Japan goes by the jus sanguinis principle, whereby one of your parents has to be Japanese to be a citizen to be a citizen yourself. France and many European countries have this policy too.
Like most open countries, though, Japan does offer refugee type citizenships, and special circumstances. And then there's standard the naturalisation process. It's quite possible, if you had gaijin parents who naturalised, to be born a citizen in a Japan, even though you, yourself are a gaijin.
And getting rid of your US citizenship is as easy as swapping it for a Japanese one.