How to use Shared Preferences in MVP without Dagger and not causing Presenter to be Context dependent?

Your Presenter should not be Context dependent in the first place. If your presenter needs SharedPreferences you should pass them in the constructor.
If your presenter needs a Repository, again, put that in the constructor. I highly suggest watching Google clean code talks since they do a really good job explaining why you should use a proper API.

This is proper dependency management, which will help you write clean, maintainable, and testable code. And whether you use dagger, some other DI tool, or supply the objects yourself is irrelevant.

public class MyActivity extends AppCompatActivity implements MvpView {

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        SharedPreferences preferences = // get your preferences
        ApiClient apiClient = // get your network handling object
        Repository repository = new Repository(apiClient, preferences);
        presenter = new Presenter(repository);
    }
}

This object creation can be simplified by using a factory pattern, or some DI framework like dagger, but as you can see above neither Repository nor your presenter depends on a Context. If you want to supply your actual SharedPreferences only their creation of them will depend on the context.

Your repository depends on some API client and SharedPreferences, your presenter depends on the Repository. Both classes can easily be tested by just supplying mocked objects to them.

Without any static code. Without any side effects.

This is how I do it. I have a singleton "SharedPreferencesManager" class that will handle all the read write operations to shared prefs like below

public final class SharedPreferencesManager {
    private  static final String MY_APP_PREFERENCES = "ca7eed88-2409-4de7-b529-52598af76734";
    private static final String PREF_USER_LEARNED_DRAWER = "963dfbb5-5f25-4fa9-9a9e-6766bfebfda8";
    ... // other shared preference keys

    private SharedPreferences sharedPrefs;
    private static SharedPreferencesManager instance;

    private SharedPreferencesManager(Context context){
        //using application context just to make sure we don't leak any activities
        sharedPrefs = context.getApplicationContext().getSharedPreferences(MY_APP_PREFERENCES, Context.MODE_PRIVATE);
    }

    public static synchronized SharedPreferencesManager getInstance(Context context){
        if(instance == null)
            instance = new SharedPreferencesManager(context);

        return instance;
    }

    public boolean isNavigationDrawerLearned(){
        return sharedPrefs.getBoolean(PREF_USER_LEARNED_DRAWER, false);
    }

    public void setNavigationDrawerLearned(boolean value){
        SharedPreferences.Editor editor = sharedPrefs.edit();
        editor.putBoolean(PREF_USER_LEARNED_DRAWER, value);
        editor.apply();
    }

    ... // other shared preference accessors
}

Then whenever access to shared preference is needed I pass the SharedPreferencesManager object in the relevant Presenter's constructor. For example :

if(null == presenter){
    presenter = new Presenter(SharedPreferencesManager.getInstance(getApplicationContext()));
}

Hope this helps!