You can go for the speed issue like Aakash Mallikdid. And I am not sure if I would even consider it because react is itself is not really fast unless you know what you're doing.
So I will argue about the problem of state and separate points of truth.
if you change the DOM outside of react and react does not know about it, react won't be able to get the same result on the next rendering iteration.
what you could do in theory is move the state outside of react in something like redux.
so JQuery does something -> statecontainer gets the update -> react will do something accordingly.
in theory react is just a view library, so you could use jquery to build your framework and render everything with react still react can only "see and hear" what's happening in react. it's functional so it does not care about the global state unless you patch it in.
Taste in the end. I would not use jQuery in react unless it's really necessary, which it's probably not.