I switched my Activity to a AppCompatActivity and now calling invalidateOptionsMenu() in onOptionsItemSelected() no longer updates the Menu items as they did before. onPrepareOptionsMenu() is not called.
I added the following dependency
compile "com.android.support:appcompat-v7:22.2.1"
And updated my Activity to a AppCompatActivity (note only the first call to invalidateOptionsMenu() in onResume() works, the the other two do not):
public class MyActivity extends AppCompatActivity {
    private boolean isStopSaved;
    // ...
    @Override
    protected void onResume() {
        super.onResume();
        if (/* Check DB if star should be set */) {
            isStopSaved = true;
        } else {
            isStopSaved = false;
        }
        invalidateOptionsMenu(); // This updates the menu as expected
    }
    @Override
    public boolean onPrepareOptionsMenu(Menu menu) {
        // ...
        return super.onPrepareOptionsMenu(menu);
    }
    @Override
    public boolean onCreateOptionsMenu(Menu menu) {
        getMenuInflater().inflate(R.menu.menu_schedule, menu);   
        return super.onCreateOptionsMenu(menu);
    }
    @Override
    public boolean onOptionsItemSelected(MenuItem item) {
        switch (item.getItemId()) {
        case R.id.menu_starred_add:
            isStopSaved = true;
            invalidateOptionsMenu(); // Does not update menu
            break;
        case R.id.menu_starred_remove:
            isStopSaved = false;
            invalidateOptionsMenu(); // Does not update menu
            break;
    }
    return super.onOptionsItemSelected(item);
}
Edit: My device is running Android M Preview 2.
You should call supportInvalidateOptionsMenu(), which is meant to work with the support libraries. 
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