Is a Rails 5/react.js app only using GraphQL feasible?

I'm building a new app: rails 5 for the backend, react.js (actually Gatsby) for the frontend. Is it possible/desirable to do it all using GraphQL and skip REST endpoints entirely?  

Of course it is. If that's what makes sense for your application. GraphQL APIs are far more flexible. Here's a great gem for building a GraphQL API in Ruby: https://github.com/rmosolgo/graphql-ruby.

If you need Relay, I believe you have to pay for the pro version though.

looks good, But for "Pro" version, $900/yr ??? http://graphql.pro/ Are there other, less expensive, ways of doing GraphQL in Ruby that people here recommend?

Really, if you don't use Relay, you won't need the pro version. That's the only GraphQL gem I'm familiar with, though.