None of the royals are actually racist, least of all against the Japanese.
It is Britannia's outstated philosophy of "the strong survive, the weak perish" that is the cause of Britannia's racism. The royals are the strongest and thus hold little or no prejudice based on race, but rather, on ability. It is those lower down the ladder, the ones who cannot come to terms with their own weakness, who are racist. The commoners of Britannia are likely to be very racist, because they are the lowest class. They are the ones who are the weakest in Britannian society, and Britannian society despises weakness. Therefore, rather than accepting their weakness, they instead claim that other, conquered areas and their inhabitants are weaker due to their heritage, in order to elevate themselves. A great many Britannians are probably just like Nina: xenophobic and convinced of the inferiority of the Elevens or the Tens or the Eights, because they themselves are labeled by Britannian philosophy as worthless, and they run away from that by bullying those they consider "lesser."