As you may know, Japan has no national civil or criminal legislation outlawing and punishing racial discrimination, meaning businesses with "Japanese only" signs aren't doing anything illegal.
Problem is, I'm not sure it would matter if such a law existed.
To illustrate, consider one business sector that — technically — cannot exclude customers by race or nationality: hotels. Article 5 of Japan's Hotel Management Law (ryokan gyoho, or HML) says that licensed accommodations cannot refuse service unless 1) rooms are full, 2) there is a threat of contagious disease, or 3) there is a issue of "public morals" (as in shooting porno movies there, etc.).
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