For it to be a preference over Shariah, Shariah must be an option, and it hasn't been. It has been an option between residing in the Democratic West, and residing in a Secular Junta or Monarchy backed by the Democratic West.
Majoritarianism doesn't mean much, since at least in places where voting is optional, majorities never decide anything. They're pluralities of the general population, since at least half of humans understand math and proceed not to vote. Since majoritarian mob-rule democracy doesn't exist, we - the plurality-creating minority - can happily move on towards which type of fascism we prefer.