I've been using Apollo Client and React to manage state on a medium size React app (i.e. no Redux). Interested to hear your thoughts here. Have you been using Redux + Apollo Client + React on a medium to large app?
Introducing state management doesn't come for free, of course. That is an extra layer of complexity that you have to reason and maintain. And if your app doesn't need any client side caching or you don't envision a need to have shared state between your components maybe you don't need to have something like Redux. But I feel like the use cases for those sort of apps tend to be pretty narrow.
edit: Another commenter mentioned a good point that gets to the heart of your question better than my rambling -- You are still managing state in your app - just with Apollo instead of Redux.
So yes, you can replace Redux with something different. There are pros and cons to it, but it's not required or even fundamental to implementing GraphQL in a React app
There are some new features in Apollo for handling client side state but I'm sticking to Redux for now (for client side state, I am using Apollo for some data fetching).