I think the only reasonable way to use GraphQL on a freely accessible server is to only allow a set of whitelisted queries, ideally automatically extracted from the frontend codebase, stored on the server and invoked by id and arguments.

This essentially turns GraphQL into a DSL for implementing REST endpoints, which is still a useful thing since it allows to write the REST endpoint with only knowledge of the GraphQL API rather than knowledge of the whole backend architecture, which is generally useful if the backend and frontend are written by different people or teams.

That's the way Facebook uses it on their main website: they pass the query id in the "doc_id" form field, the arguement in the "variables" field, the server gets the actual GraphQL query based on the doc_id from some sort of internal dictionary and AFAIK no GraphQL query string ever goes on the wire in production.