NetworkManager spawns two of same prefab

I have a 2D multiplayer game with a character selection screen and script that carries the selection to the next screen where both players spawn. The only problem is that each client sees both themselves and the other player as the same model, rather than different models depending on which one each player picked.

The prefab I use in the NetworkManager is called CharacterList and has my player game object prefabs as children. Players see themselves as the correct character but the opponent is always the identical character model. For example, if I have a red character and a blue character, both characters on one screen appear blue, while both characters on the other screen appear red.

Here's my character selection script which is attached to CharacterList:

  public class CharacterSelection : MonoBehaviour {
  
      private GameObject[] characterList;
      private int index;
  
      private void Start () {
  
          index = PlayerPrefs.GetInt ("CharacterSelected");
  
          characterList = new GameObject[transform.childCount];
  
          for (int i = 0; i < transform.childCount; i++)
              characterList [i] = transform.GetChild(i).gameObject;
          
          foreach(GameObject go in characterList)
          {
              go.SetActive (false);
  
              if (characterList [index])
                  characterList [index].SetActive (true);
      }
  }
      public void ToggleLeft()
      {
          characterList [index].SetActive (false);
          index--;
          if (index < 0)
              index = characterList.Length - 1;
          characterList [index].SetActive (true);
      }
      public void ToggleRight()
      {
          characterList [index].SetActive (false);
          index++;
          if (index == characterList.Length)
              index = 0;
          characterList [index].SetActive (true);
      }
      public void ConfirmButton()
      {
          PlayerPrefs.SetInt ("CharacterSelected", index);
  
          SceneManager.LoadScene ("MultiplayerBranch");
      }
  }