Islam is compatible so long as all other societies bow to their muslim masters. Of course, the primary Islamic state, the one EVERY muslim prays to five times a day, does not permit Jews to enter its borders, non-muslims to practice their religions, nor non-muslims to enter the segregated city of Mecca.
Who are these "moderate" muslims again? They certainly don't speak out against such injustice, instead they pray to it.