No different from Europe during much of the Medieval period.
How much luck do you think we would have had trying to "civilize" the bickering, quarreling, bloodthirsty warlords that popped up in Western Europe in the 6th and 7th centuries, after the Roman Empire went kaput? Or even in the 12th century when the ultra-superstitious Catholic Church ran things and people were afraid to take baths or open their windows at night for fear evil spirits would carry them off? We'd have been branded heretics or witches and burned at the stake. Europe had to go through that to get to the Magna Carta, the Enlightenment and Reformation, and then through how many wars and convulsions to get to where it is today?
Islam is where Christianity was back then. They're going to have to sort through the same mess of theological crap that Europe/Christianity had to. No one can do it for them. We can't force them to regard women as human beings, or to believe there are better ways to resolve political disputes than jihad and war, or to recognize the value of scientific inquiry and the limitations of religious dogma. We can't bomb them into separating mosque from statehouse and court.
The Catholic Church wasn't superstitious, and denounced the very idea of witches existing, in fact, as superstition. The Church also had next to no power to run much of anything in the 12th century. The 11th century was basically 100 years of Church reformers thinking they might be able to run things better and everyone else around them convincing them they could not. If we were to go back and try and get bickering nobles to stop fighting each other for no real reason, we'd be labeled priests instead of heretics, since that's what the Church was all about for the longest time. It is the Reformation itself in fact that sparked the witch craze and greater power of the Church - but especially Protestant Churches - in government affairs.
Islam is not back in the 12th century. If we had to force ourselves into a false comparison at all, it'd be closer to the 18th and 19th century. They regard women as human beings, just not as men. The current neurosis regarding patriarchal role in the Middle East has less in common with Medieval mores and far closer to upper class Victorian England. They developed other ways to resolve political disputes by the 14th century like everyone else, and developed it further by the 17th century parallel if slightly lagged with Europe. There was already value to be found in scientific inquiry from the 8th century, and the limitations of dogma were already evident to them by the 9th. The Saudis themselves, fanatical and dogmatic more than any other at the time, immediately sought to acquire economic deals with Roosevelt to set up oil production, develop infrastructure and academies of science, and modernize their army. The fanatics that did want to fight like they always had done were actually corralled up and shot up after that.
The mosque was never state or court as well. Except for a few Ismaili Shi'a experiments and some heresies in Morocco the 'mosque' was always separate from the apparatus of state. Religious scholars that signed on with governments were there to act as propaganda and public affairs officials since all the states of the Middle East except for the Sharifs in the Hedjaz and the late development of the Morroccan and Ottoman dynasties into stable, legitimate dynasties were military despots and dictators usually of foreign ethnic backgrounds.
I guess what I'm trying to say is:
But you have to consider what the alternative is...as we're seeing now, the Egyptians voted in a Muslim fanatic whose platform involves unwinding the past couple centuries of social progress there.
This is actually wrong. There are some Salafis that want a regressed society, but Islamists and Islamism is a political movement that is forward thinking. When Khomeini established his rule in Iran for instance, it wasn't a return to anything any cleric at the time recognized. He had to write a defense of his vision which most of the scholarship in Qoms still doesn't actually buy, and is a lot closer in theory to Plato's Republic
than anything in Shi'a theology. We need to understand that movements like the Muslim Brothers are a completely modern phenomenon, and to say they wish to return to the Medieval Age would be the same as stating the Nazis wanted to bring Germany back to the age of Germanic pagan tribes and Teutonic knights. The things they espouse are modernized answers to modern social problems and worries in modern Muslim societies. In a way it's like Zionism was for Jews, a form of religious nationalism that glorifies a romantic past but can and will ignore theology developed since then so long as it suits their vision.
Back to the Tale of Drones and Polio, there isn't anything religious or cultural at work here. Due to a lack of professional media, word-of-mouth conspiracy theories form faster than maggots on a corpse. It is believed that the U.S. uses aid workers as spies, likely because of the role one spy played in finding Bin Laden, and so believes the U.S. is using this intelligence gained from these secret agent-doctors to launch drone strikes against leadership in the Taliban. Thus the logic is so long as drone strikes are still being carried out, UN relief workers sent to treat polio and other diseases in the region will not be welcome in case they are there to gather intelligence on the side. It's not actually an ultimatum. There's no overt threat being made, no demands, and no promise of a return to normalcy if a condition is met. This isn't comparable to a situation in Africa where many locals actually distrust doctors and modern medicine - there's no belief that polio vaccines don't work or that they're 'of the devil' or something like that. It's pure blacklisting of what they believe to be a compromised organization that until now was considered neutral like journalists.
It wasn't that we left these countries to rot, but rather that their underlying religious and culture systems were not compatible with liberal industrial democracy.
If true, at all, then the majority of Muslim nations after colonialism ended would have been traditional tribal federations. Instead they were all with the exception of the Gulf States liberal democracies with developing capitalist industries, middle classes, and
popularly demanded and legislated women's suffrage rights. And when they gave up on democracy, they didn't revert to anything traditional at all but instead accepted a series of national socialist military dictatorships - another completely western ideology. Even Iran under the ayatollah was adopted as a republic with a constitution setting laws for an elected parliament, continued the right of women to vote, and guaranteed religious minorities seats in parliament and (on paper at least) equal citizenship with no restriction on right to hold office or be levied with a poll tax.
And many of the early leaders and politicians that handled the transition from colony to independent state were religious scholars themselves extolling the new civic culture and nationalist movements. A culture incompatible with modern political theory would not have bought into it the systems for more than a decade at best. Instead we've had three generations pass. The Middle East actually took off running with the idea - they just didn't get to develop stable civic institutions before the military despots began overthrowing everyone and suppressing healthy civic culture for decades in the name of perpetual war with Israel/Iran/India/Western colonial powers.