Not being at all fluent in Japanese, I will say all things are possible, even for a foreigner. If you have Bushido, their Samurai rules still apply culturally... round eyes or not...
The Japanese are very “prejudiced,” but not in a context of ethnicity, it is cultural... they revere exceptional people...
You're right. They have little time for non-conforming, whining foreigners, but if you display perserverence and an inner strength to achieve a goal (especially learning their langauge and/or culture), you will be accepted into their "cultural" group and racial differences will fade. I have often discussed this with my in-laws, that despite our appearances we no longer, for a long time now, look at each other in a racial context. The same goes for another friend and his family, who's father, a former Imperial Navy sailor, always enjoyed me coming to his house and drinking sake with him.
The Last Samurai is an excellent example, albeit a fictional story loosely based on events of the Meiji Restoration. But I may just be "oblivious." ;^)