I think we can expect to convert most of the Islamic world to "progressivism" - not the silly version of it, but the same more sensible version that most Americans share - over time, though.
Yet observe. The high points of what you would call sensible progressivism in the Muslim world were during the crusades, and during the colonial era - and during the colonial era, they got their progressivism from rule by the likes of Lord Cromer, who most Europeans in 1907 viewed as horrifyingly reactionary.
And since the days of Lord Cromer, Muslims have been becoming less and less progressive. What makes you think this trend, displayed most recently in the mass rape and sexual mutilation of Lara Logan, and similar treatment of large numbers of Coptic Christians while the world averts its gaze, is going to reverse? Female circumcision and so on and so forth is increasing, not decreasing, and has been ever since the colonial tide receded.
The underlying forces driving this trend is that sensible progressivism is not sensible, but vicious and suicidally crazed - most people in 1950 or so would have considered the sensible progressivism of 2000 or so as completely insane, and most people in 1910 would have considered the sensible progressivism of 1950 or so as completely insane, and most people in 1840 or so would have considered the sensible progressivism of 1910 as suicidally insane. It was the people in 1840 whose sensible moderate progressivism successfully influenced the Muslim world, and if you want to succeed in moderating Islam, you have to return to what people in 1830 or so considered moderate progressive.
This is the same sort of thing that explains why in a small Canadian town, a woman of Native American origin was brutally raped and murdered, and it was claimed that the "whole town", more or less, knew who did it, and yet it took years for the police to complete their investigation, and bring the perpetrator of this heinous deed to justice.
Perhaps because the whole town did not know who did it, and it is probable that the guy who was scapegoated for the deed did not do it. That story is a load of baloney, similar to the Duke rape case and the "lynching of Emmet Till for whistling at a white woman"
Exterminating the Muslims of the world for the crime of being no better than us seems a bit unfair.
When we had the upper hand, during the colonial era, there was peace and justice - or there was once Muslims submitted, though the means employed to obtain submission were apt to be drastic. When Muslims had the upper hand, for example 1400 to 1700, there was mass state sponsored rape, widespread enslavement of white Christians, and frequent mass murder. Compare the treatment of Muslims in Egypt when Christians ruled, with the treatment of Copts in Egypt today.
And supposing, as good progressives believe, that there was no peace and justice during the colonial era, that we are no better than they. Then they would be bad enough that it would necessarily be war to the knife. Whether or not we are better than them, it is better for us that we win than that they win.