You can see it happened in the secular Republic of Turkey. Yes Turkey almost 100 percent Muslim but millions have demonstrated against the ruling party's Islamist practices. They do not want sharia law.
Journalists, retired and active military, professors, anyone who opposes the AK Party and the Islamists are arrested and jailed accused of all kinds of crimes against the state.
Some say the whole Islamist infiltration in Turkey was encouraged by the Gulen Movement headquartered here in the States (Pennsylvania).
It is happening here, whoever is doing it. Only one day they are going to yank a little too hard on the junk yard dog's chain. Then, "Pow! To the moon, Mohammed"
There are many aspects to things Middle Eastern that affect modern Turkey such as who is going to dominate.