Well fundamentally, its main reason for backwards laws (e.g. non-equality for women) is that the House of Saud derives its legitimacy from a rather orthodox religious sect, in exchange for enforcing said orthodox sect's backwards religious rules.
Switching to a democracy would mean nobody need pander to the Wahhabi sect.
Sure. That's exactly what happened in e.g. Egypt /s it didn't.
We have to face the reality here; if the "religious sect" is so powerful that it can challenge the absulotist monarch, then it's definitely powerful enough to play divide-and-conquer with different democratic parties.
Switching to a democracy would mean nobody need pander to the Wahhabi sect.