I'm inclined to cleave towards Tassa Kay's viewpoint: the Clans at this point aren't the monolithic entity (yeah, I know that was never the case) they were circa 3050. Honestly, saying that there are overarching Clan philosophies is largely a fool's errand. As far as I can see (and I haven't read much of anything in the ilClan era), there are Clans that rally behind Clan Wolf's ilKhanate, those that deny it as legitimate, and (most importantly) those who don't care. The Rasalhague Dominion is not, AFAIK, about to cede any territory nor sovereignly just because the Wolves took Terra. The Scorpion Empire is just out on the periphery surviving, the Sharkfoxes are settling into their role as Comstar 2.0, and the Raven Alliance is its normal inscrutable self. If I were asked to group these disparate groups into 2 or 3 easily-determined philosophies, I'd quit--it's largely impossible. IMO, none of the definitions work--at best I'd say there are 2 camps, the self-deterministic (Rasalhague, Scorpion, Raven) and the traditional (Wolf, Jade Falcon, Hell's Horses). Spirit Cats would be the former, Nova Cats would honestly be closer to the latter than they'd admit.
There's my (admittedly sloppy) analysis of the situation.