A recent look into a Dwimmermount preview got me thinking about this question.
As far as I understand it, the core rulebook talks about domains generally, without reference to explicit classes except in the case of demi-humans. Fighters, clerics, and mages are explicitly talked about ruling domains, and clerics and mages are referenced ruling domains in the divine power and sanctum rules, respectively. Thieves, however, are only referenced building hideouts, which are secret and cannot rule a domain.
This seems pretty clear-cut, but I saw in Dwimmermount that one of the realms, Yarm, is ruled by a Lord Syndic, an 8th level Venturer. Also, in Axioms 3, the rules for domains and land ownership are written in a class-neutral way.
My big question is, what's stopping a thief (or bard, or venturer especially) from deciding to buy/build/steal a castle and start issuing orders?