Idiomatic React is both compatible with and orthogonal to state management libraries like Redux or MobX. React is (in my opinion, and likely in the opinion of its creators and maintainers), a library for creating reusable ("dumb" or "presentational") components. In many web apps built with React components, you will want another library to manage the global state of the entire application and provide your dumb components with read/write access to specific pieces of that global state.

I don't understand your point that injecting state into your components (e.g. with Redux' connect function) means JSX is just another fancy HTML templating library. All you need to do is have your React component export a "dumb" version as well as a connected version. Your dumb version will still be reusable in other parts of your application, and any other application could also use your dumb component and connect it to their global state through whatever means they please.