The way I see it . . .
Separation of church and state has taken place very recently in many Western countries and not at all in some of them. Sweden achieved it in 2000, and the English church (as distinct from Irish, Welsh and Scottish churches) is still not formally separated with some secular power remaining through voting rights in the English parliament to this day.
It's important to recognize that Islamic law was far ahead of many Western states in many respects from medieval times until quite recently, such as property rights for women. It is tempting to see all the problems of the Middle East as stemming from the prevalence of Islam. However, most of the problems seem to originate from extremists twisting the writings of modern Islamic mystics to their own power-seeking purposes, causing Islam to evolve backwards towards its origins as perceived by some.
There isn't a single ME country successfully practising western-style democracy tha I know of - including in some respects Israel. Most of the ME has been subject to ruthless foreign rulers since Roman times, some countries until well into the 20th century. I don't think the solution is an English style constitutional monarchy such as was attempted in Egypt or a US-inspired democracy such as is being tried in Afghanistan and Iraq and any other form of Western-style practice. The form of government has to come from the people of each country, and will be different for each country and people, just as it is different for each western country. Only this way can a country's government be compatible with the culture of its people.
It's axiomatic that each ME country wants to compete with modern democracies in efficiency, influence, national pride, cultural self-sufficiency, internal security and external power. It is an Islamically-dominated area and Islamic solutions are seen as desirable by a majority of people and leaders. Just as most European democracies grew from Christian-based and -supported monarchies, so ME governments will not survive without the support for, and recognition of, Islam.
And that's were the heart of the problem lies.
From my admittedly limited research, Islamic law (Sharia) seems to lack many of the crucial features of modern (20th century) Western legal systems that are required to harness the full power of people and national economies, such as full equality and protection under the law for women in all respects as for men, and the lack of recognition of legal entities other than actual people which permits the establishment of a limited liability corporation. It's not surprising that it hasn't evolved to embrace modern concepts, as it is hardwired into the basic writings of islam.
So it's not just the governments and the cultures that must progress, it's the law which for most ME countries is currently enshrined as a religiously-controlled entity rather than a progressive set of rules that are, at least nominally, equal for all and permissive of economic and cultural progress. Equivalent change in western societies has taken centuries; it will be a major achievement if the region achieves anything remotely resembling stability within the lifetime of any of us.