Once you buy into the Flux methodology (not necessarily Flux as described by Facebook), a lot of the concerns that Backbone handles melt away. You don't need observable collections and models because all state changes are explicit and data moves in just one direction. Given that Backbone's core is just a thin layer on top of XMLHTTPRequest, you're better off just doing XHR yourself, with POD objects for data.
In my React-based apps, I typically include react-router for routing and request or superagent for ajax calls. You can also include a Flux-inspired library if you're into that sort of thing.
That's how I do things, React + raw Xml Http requests. Since JSX is already a layer on its own no need to add yet another layer of complexity.
Of course you would need to do things like ajax or routing, for which there are endless libraries, or you can just go pure XHR. React-Router is terrific for routing.