I have no love for Islam. None at all. As bad as Islam is, however, it is not a "threat" in any meaningful sense.
The Islamic cultures are to a greater or lesser degree, barbaric, misogynist, and fundamentally intellectually bankrupt. The only possible exception is Turkey with an explicitly secular, non-Islamic government. Even in Turkey, though, Islam has a negative effect on its national culture. Islam, unlike Christianity and Judaism, has not yet engaged in sufficient sophistry and bullshit to even partially insulate the daily life of individual believers from the absurd, barbaric and misogynist elements of its scripture.
I am opposed to Islam primarily because of the suffering endured by its believers, especially women. They suffer not because they actually believe the Islamic way is a good way of living, but because they falsely believe they will go to Hell if they do not sacrifice their happiness and well-being in this life. Only the threat of hell could possibly justify the human cost of Islam.
All this being said, Islam is not much of a threat to the West. Precisely because Islam is so horrific, so intellectually bankrupt, Islam has neither the political, social, technological or military power to directly threaten the West in any substantial way. The "threat" of Islam is indirect: Authoritarian, anti-democratic elements in the West are promulgating fear of Islam—as opposed to justified disgust and disapproval—to undermine the West's liberal, Enlightenment and democratic values. But there's little to fear, and what there is to fear is relatively easy to deal with.
The idea that Islam could use military power to invade and overthrow even a single Western nation is risible. Even if the Islamic nations were able to cooperate (and sectarian and nationalistic differences prevent such cooperation) it's doubtful that they could militarily defeat even tiny Israel. It's not enough to simply buy high-tech weaponry; you have to have a pervasive pro-technology attitude in the soldiery to effectively employ such weapons; the very nature of Islam excludes a pro-technology attitude. Fanaticism, too, is greatly overrated: Fanatics make great suicide bombers, but poor soldiers. The whole point of war is not to die for your country, it's to make the enemy die for his.
Nuclear weapons do not serve any offensive military purpose; they are useful only as a deterrent. It's instructive to note that there have been conflicts with almost every possible nuclear match-up, from the US vs. Iraq to Britain vs. Argentina and India vs. Pakistan, and nuclear weapons have never provided an offensive advantage. A nuclear armed Iran, for instance, does not in any way plausibly increase the military threat to the West, even Israel: Iran knows that if it were to use nuclear weapons against Israel, it would face certain retaliation and complete destruction. Not even an Islamic government would be so blatantly suicidal.
Terrorism (or what James might call "violent activity by non-state actors") and other forms of guerrilla action are very limited tactics, useful only for narrow political purposes. And the political targets that terrorism can actually affect are primarily those—such as imperialism and colonialism—which are ethically indefensible in the first place.
Islamist terrorism (or even Christianist terrorism) is still, of course, a matter of considerable concern. But the threat is not "existential": Terrorist activity does not have the power to destroy governments or democratic institutions. Terrorist activity can be effectively countered by modifying ethically indefensible foreign policy in conjunction with ordinary police work subject to traditional democratic, liberal constraints.
The threat of immigration and democratic "take-over from within forms" is hardly a threat. Even with massive immigration, the Muslim population of Europe (outside the Islamic nations of Turkey, Albania and Bosnia-Herzegovina) is less than 5%. Israel is the only liberal democratic country with a substantial number of Islamic residents, a problem which would be quickly solved by partition and Palestinian statehood.
The social problems caused by the level of immigration that does exist are difficult but solvable. Multicultural integration—focusing on second- and third-generation bilingualism, economic integration and uniformity of law while preserving benign components of immigrant culture—are strategies with a proven history of success in the West. Even the worst sorts of bullshit multiculturalism (notably ghettoization and separate law) merely exacerbate the social issues and show an indefensible indifference to the suffering of immigrants; they do not raise the threat of internal takeover of a few percent of the population in any meaningful time frame. The demographic landscape might well change in the next half-century, but it's impossible to make meaningful social prognostications on such a long-term time scale.
The only meaningful threat posed by Islam is indirect. By promulgating fear that is entirely rationally unjustified, authoritarian elements—especially Christian Dominionists—in Western cultures can scare the population into abandoning the liberal, democratic institutions and ideologies that are the basis of the West's scientific, technological, social and humanitarian success. Such fear can justify only authoritarianism and imperialism and bring out the worst elements of our own national character.
Islam is, in this respect, merely a decoy. The authoritarian measures "justified" by a response to Islam and Islamist terrorism will be immediately employed to suppress local, democratic dissent and impose ideological (probably Christianist) uniformity. If we do not panic, we can deal with the all the badness of Islam using the proven and ethically defensible ideals of Western liberal democracy and concern for individual human rights.
 Partition and statehood would admittedly create other problems.