Representative government isn’t necessary to being a republic. Most republics have partially representative governments, but the term most broadly refers to any government that isn’t a monarchy (and I would probably count “fascist tinpot dictatorship” as a monarchy of sorts). Popular representation was a very small deal in the Roman Republic, which is the basis for American republicanism. China is probably still technically a republic, albeit a very authoritarian one.
Also, I don’t see anything wrong with California that isn’t reasonably common in many of if not the bulk of the other 49 states. Certainly the Republikan Party would have lost significantly more seats in the House of Representatives if the House weren’t so gerrymandered to make competitive races nearly extinct. That pretty much means every state is doing what California is doing.
@ml3269: there isn’t really anything unusual about California except for its size. It’s a U.S. state in every sense of the word. It doesn’t even have an especially unique legal system by U.S. standards, unlike Louisiana.