...that half of majority-Muslim countries make Islam the state religion?
Of the 46 countries in the world with majority Muslim populations, 23 declare Islam to be the state religion in their constitutions. The rest either proclaim the state to be secular or make no pronouncement concerning an official religion. The 23 countries where Islam is declared the state religion are: Afghanistan, Algeria, Bahrain, Bangladesh, Brunei, Egypt, Iran, Iraq, Jordan, Kuwait, Libya, Malaysia, Maldives, Mauritania, Morocco, Oman, Pakistan, Qatar, Saudi Arabia, Somalia, Tunisia, the United Arab Emirates, and Yemen.
Under international standards, a state may declare an official religion, provided that basic rights -- including the right to freedom of thought, conscience and religion or belief -- are respected for all without discrimination. This means that the existence of a state religion cannot be a basis for discriminating against or impairing any rights of adherents of other religions or non-believers or their communities. Unfortunately, in practice many states with official state religions do not meet this test.
For more information, see USCIRF's recent study, The Religion-State Relationship and the Right to Freedom of Religion or Belief: A Comparative Textual Analysis of the Constitutions of Majority Muslim and other OIC Countries .