FileStream/BinaryFormatter save static variables without PlayerPrefs

Keep your runtime classes totally separate from serialization data classes and there will be no issue, for example:

runtime state classes:

 public class MySceneController : MonoBehaviour
 {
     public static int Score = 0;
 }
 public class Player : MonoBehaviour
 {
     void Awake () {}
 }

serialization data class (what is being saved):

 [System.Serializable]
 public class GameState
 {
     public int player_score;
     public Vector3 player_position;
 }

then:

 var gameState = new GameState();
 gameState.player_score = MySceneController.Score;
 gameState.player_position = player.transform.position;
 /* code that serializes and writes gameState to file */