They aren't a traditional clan in a sense of customs, but rather in wanting to keep the nation's structure in place.Why? Why? Kunoichi Red is an old pre-Meiji low aristocratic clan, in a world where Japan did not fight the Second World War and all the old structures are still in place.
How would a traditionalist clan have a Versailles-like headquarters? I always imagined them as a mixture of fashionistas (they work in the entertainment media) and traditional geisha.