Having actually lived in a Muslim country
I think I understand its appeal.
Islam brings peace, stability, and an orderliness in society, and instant membership in an international club of 1 billion plus, with all the benefits that brings. A Muslim anywhere in the world has Muslim allies everywhere in the world. Crime is much lower in an Islamic society. Men, women, merchants, workers, teachers, political and religious leaders, and everybody else in society has a lot fewer questions and ambiguities to worry about in life. Islam gives guidance and has the answers for everything. There's a lot less hard thinking to be done.
In short, it's got all the great advantages of every other form of totalitarianism.