Read the whole article, and read Douthat's first. But understand that this is a dangerous opinion - "Muslim Extremists are bad." "Some Muslims are extremists." "Therefore we must wage war against all Muslims," and ask yourself how this is compatible with Jesus' teachings ("Love your neighbor as yourself," "Turn the other cheek," "Let he who is without sin cast the first stone," etc.)?
It's obviously true that some Islamic extremists are inherently incompatible "with the Western way of reason," but that's just as true of Christian extremists and Jewish extremists and a whole array of other kinds of extremists. And some measures taken in the name of accommodating Islam are in tension with core liberties -- just as laws enacted in order to impose Judeo-Christian dogma are.
But the claim that Islam itself -- and the world's 1.5 billion Muslims -- cannot be accommodated by, or peacefully co-exist with, Western values or Christianity specifically is bigotry in its purest and most dangerous form. It's hard to imagine anything more inflammatory, hostile and outright threatening than a call for Christians of all denominations to unite behind the common cause of fighting against Islam as Christianity's most "enduring and impressive foe." No more "conciliation" or appeasement. What, exactly, does Douthat have in mind for vanquishing the Islamic menace from Europe? What weapons will this "united Anglican-Catholic front" employ against its reason-hating enemy? Which "accommodations" of Islam exactly should cease?
BTW, Glenn's updates show western Christian examples that are not necessarily compatible with "the Western way of reason."