If you want to get technical, they're archaeo-galacto-imperialists, because they still worship the Old Gods from Afar, and continue to serve the unbroken dynasties that sprung from the Old Gods' loins in the days when humanity was still just a bunch of single-celled organisms cruising through space on frozen asteroids.

Of course, they serve as deified emissaries of the Old Gods, giving them a position in the universe incomprehensibly far above us lesser beings who have never even heard of the Old Gods and have no clue where "Afar" even is. But it is a service they render with great pride and deference!

Cats are anarcho-monarchists (if more than one cat present)

humans are free to not serve cats
not the cats’ fault they’re irresistible