What do al Saud and their followers think about their government's policies to destroy and demolish heritage sites?

Can you be more specific and give examples?

Al Saud and their followers in my opinion are too engrossed with life's enjoyments and the activities aiming at keeping up their privileges at all costs to realize the implications of what they have done. Their case reminds me of this story related by the Fountain of Knowledge (Imam Ja'far Al Sadiq): “In ancient times there lived a man who sought to earn his livelihood and procure great wealth by lawful means but was unsuccessful. He then strove to achieve his objectives by unlawful means but once again failed. Satan appeared before him and said to him: “You tried to acquire great wealth by lawful as well as unlawful means but were unsuccessful. Do you want me to show you a way by which you would not only become wealthy but you would also attract numerous followers?” The man expressed his willingness to know how he could get rich. “Concoct a religion and invite people to follow it,” suggested Satan. The man fabricated a religion and soon, he had a lot of followers through whom he became rich. One day he realized that he had made a mistake by leading numerous people astray so he resolved to inform the people of the falsity of his religion and the error of his ways. But however hard he stressed and emphasized, the people simply refused to accept his word. “Your previous views were correct; have you become skeptical of your own religion now?” they asked. When he heard these words, he got some shackles and chained himself. He pledged that he would not unchain himself until Allah accepted his repentance. Allah revealed to the Prophet of the time to convey the following message to the person: “By My Honour! Even if you weep and supplicate to the extent that every ligament of your body falls apart, I shall never accept your prayers, till you inform those people who have died after having been led astray by you of the reality and they turn back from your religion"

They are following their ideology that does not allow for 'innovation' in religion.