Islam is opposed to the separation of church and state.
Eh, and so is Christianity generally. So much so that we do not even have separation of church and state in Denmark: the Church of Denmark is the official state church, which is written into the Constitution. There is freedom of conscience and worship, but one religion (Lutheran Protestant Christianity) is officially established, while the others are (according to the Constitution) merely tolerated, allowed to worship as they wish "provided that nothing at variance with good morals or public order shall be taught or done" (section 67).
Of course, in practice the church has lost almost all of its power in a gradual reform process spanning the past few decades. But I don't see this as some bit fundamental disagreement between Christianity and Islam, more a practical issue of which parts of each religion are dominant and what kinds of political power they have. In the current era, the temporal power of Christian theocrats is waning, so they are no longer much of a practical threat. But not because Christianity is doctrinally particularly great. Christian conservatives simply lost the political battle; if some things had turned out differently, they might have won, or at least come to more of a stalemate. But they didn't.