There are many possible fixes. The most obvious is to wrap it in a mutex (assuming 'done' is standing in for much more complex logic):

  func main() {  
      doneMutex := sync.Mutex{}
      done := false
  
      go func(){
          doneMutex.Lock()
          defer doneMutex.Unlock()
          done = true
      }()

      getDone := func() bool {
        doneMutex.Lock()
        defer doneMutex.Unlock()
        return done
      }
  
      for !getDone() {
          runtime.Gosched()
      }
      fmt.Println("done!")
  }

Another option would be to use a channel in place of done.

Effectively, the lesson here is that go doesn't have concurrently safe types (e.g. no concurrent map) nor generics to create them, so all concurrent code must be built around the builtin generic concurrent-safe type (channels) or must make careful use of mutexes / the atomic package / etc.

Idiomatic concurrent go either is built around channels or mutexes, and in either case the compiler won't tell you if you messed up, only the runtime race detector and testing will save you.

The fix that's probably closest to the author's intent is to use an atomic. There's no atomic boolean in the language, but if you store 0 or 1 in an int32 it works.

A single-item-buffered chan is probably most common, but a sync.WaitGroup w/ a 1 add can work if you don't need to do other ops while waiting.