Yeah like Kaiser said, there's no indication that there is a Monarchy in Japan. Supplemental materials I believe say that Japan became a Republic after a war in the Pacific in the 40s; my best guess would be a colonial struggle between the Japanese and Britannian Empires over the Philippines.
The Kyoto House is just an informal aristocracy, a powerful cabal of Zaibatsu who outwardly collaborated with the Britannian government. They aren't actually royalty.
Anyways even if it did have a Monarchy, I doubt the Britannians would have respected it. The French allowed the illusion of Self-Rule in Indochina because they had a long term view of Assimilating the native peoples. Britannia it appears is working on a much tighter schedule, as they go to great lengths to destroy conquered cultures in order to expedite assimilation. A position with such strong cultural significance, and especially with Pagan worship, would be a no-go.
I don't mind the forced assimilation angle, or prejudice against Honorary Britannians, but I reeeeally wish they'd handled it with more subtlety. Cornelia talking about working with Kyoto House to bring Area 11 to the capacity of limited self-rule was one of the few smart things I saw about the relations between the Britannian Occupiers and the Elevens. tl;dr, Britannian occupation should be pretty callous and exploitative, but it shouldn't be as cartoonishly evil.
I think the American Occupation of the Philippines to me would give a good gamut of a lot of opinions Britannian soldiers would have:
http://historymatters.gmu.edu/d/58/