Like, I said, just threaten to nuke Mecca. That'll shut them up.
Sure, nuking what is the holiest place for the 1,800,000,000 Muslims worldwide is the best way to shut them up.
A better strategy would be to threaten to divert Saudi arms sales and other support to Qatar and Iran. Maybe enlist Al-Jazeera and others in a propaganda campaign against the al-Saud being not worthy of “protecting” the Holy Places. Remind people that they’re still at heart a bunch of Bedouin warlords who violently conquered the Hejaz and most of the Arabian Peninsula. Drop the “Saudi” from Saudi Arabia - call the House of Saud “the dictators of Arabia, the butchers of Yemen,” etc. Provide platforms to Muslims from around the world angered at the Saudi-Wahhabi influence over their mosques and their communities. And last but not least, cut off all arms sales and ban Saudi lobbyists from Washington, DC., London, etc.
None of this will happen obviously, but still.
Is there not some non-royal general in the Saudi army who can just coup these people?