React does have a little overlap with jQuery but probably not as much as it might appear. jQuery isn't designed for writing components declaratively and then checking what's changed so it wouldn't simplify the React code much at all. (Plus, React is only 55% the size of jQuery.)
You're more than welcome to use XHR however you see fit. We don't dictate that choice. For many that will mean `$.ajax` - React plays nicely with jQuery (so long as you don't modify the DOM out from under us). For others that might mean a thin library that does that the same thing.
I'm actually not sure. In a side project I'm building with React, we have been using jQuery (Zepto, actually) for XHR only and it would be nice to get rid of it completely.