Saudi Arabia is a sovereign Muslim Kingdom that enforces Islamic Sharia Laws through-out the Kingdom. I believe Western countries that follow Christianity or other religions do not have any axe to grind because after all this is an internal matter of Saudi Kingdom following their religious laws and values.
Amnesty International after all is an NGO initiated and supported largely by the west and because this is a purely an issue concerning Saudi Arabian law and order according Sharia so such NGO’s should refrain from unwelcome interference into affairs of a sovereign state.
Public executions in Saudi Arabia might be sickening to the western world so should be other forms of execution they have in their own countries.
Executions, however are definitely not a pleasant affair but any how west should learn to live with and respect laws and religions of other countries in this world that are not Muslim.