You could. The existing term is "ethnostate". Japan is an ethnostate, meaning it is made up of people exclusively (or overwhelmingly) of one ethnic background: Japanese.
There are still many ethnostates in the world, but they are shrinking. Poland and Iceland come to mind.
Now, when I discuss Quebec politics, I can say something like: “Les Quebecois want Quebec to be an ethnostate; while the rest of Canada is rushing headlong into multiculturalism. That's one of the root causes of separatism.”