This is an incredibly complicated question, and one that I think is actually more a social science or political science question than a historical one. For one thing, I'm not sure that "conservative" or "moderate" really work very well in this context, as these are normative descriptions rather than positive, independent ideologies.

I think I might therefore rephrase your question as something like, "Why is the Middle East not liberal and democratic?" For starters, in defining terms, I think separating those terms out is important. Europeans/Americans often use the word "democratic" when they either mean "liberal" or they mean a kind of democracy that is, in fact, liberal. Concepts like "freedom of speech" are, in liberal democracies, rightly recognized as being an absolute necessity to having an informed multi-party democracy. But the simply act of voting--the minimum requirement for being "democratic"-- does not make one's democratic system a liberal one.

Aside from being descriptively more accurate, separating these two features out has the added benefit of helping to get at what to Europeans or Americans is often the core political contradiction of the Middle East, and the one that I think is the basis for your question. That is, where Middle Eastern countries are democratic, they seem to rarely be liberal, and where Middle Eastern countries are liberal, they seem to rarely be democratic.

Historically, liberalism--which I refer to in the broadest possible form, including both classical liberalism as well as contemporary 21st century ideas of progressivism--is not native to the Middle East. Generally speaking (I hesitate to say "always," but it probably wouldn't be far off), liberalizing reforms when they were introduced in the region had to be imposed.

The imposition of liberalizing reforms was sometimes completed by an external power and sometimes by native autocrat. The example ne plus ultra of the latter were the reforms of Ataturk in Turkey. Ataturk's reforms ranged from the profound to the absurd. While he is probably best known for changing the script used to write Turkish from Arabic to a variation of the Roman alphabet, he also introduced the "Hat Law" which banned the wearing of the traditional Ottoman fez in preference for European-style hats. Some villages were so afraid of the impact of the Hat Law that men wore paper bowlers and other western styles in order to avoid persecution/prosecution.

That's not to say that liberalizing organic mass movements are entirely non-existent. Huda Sharawi and the Egyptian anti-veiling feminist movement are one such example. But the nonetheless, liberalization and westernization were most often forced, undertaken at the expense of local customs (particularly religious customs), and are frequently associated with a kind of bourgeois secular foreign-influenced paternalism of which Ataturk, Reza Shah and his son Mohammed Reza ("The Shah of Iran") are probably the best known examples, but I think can be said to include such varying groups as the pan-Arab socialists like the Baath Party, Habib Bourgiba in Tunisia, the FLN in Algeria, and to a certain extent (despite their anti-colonial claims) the Free Officer Movement in Egypt and Libya (i.e. Nasser and Gaddafi.)

I think the fundamental historical context in which to approach this historical reality is 1. Islam and 2. colonialism/imperialism. Though certainly controversial and by no means the last word, my own thinking on this question is to give primacy to the nature of Islam in discussing the lack of liberal democratic norms in the Middle East than to over-emphasize imperialism. While foreign imperialism often tried to anti-democratically impose liberalism in the region, the same could be said of other regions that today can broadly be described as democratic and liberal, and from which the Middle East seems to stand as a stark exception. Nonetheless, the association of imperialism with liberalism, and therefore of anti-imperialism with anti-liberalism, remains a potent legacy of the imperial era in the Middle East.

Assuming that to be the case, what then about Islam is unusual in resisting democratic liberalism? Here I mostly follow the works of writers like Shadi Hamid and his book Islamic Exceptionalism. Islam, basically uniquely, is a totalizing religion. Fundamental liberal concepts like the separation of Church (or Mosque) and State simply don't apply. Where Christian Europe developed clear conceptual distinctions between secular and religious law, Islam firmly resists such distinctions because it specifically speaks to theoretically "secular" questions like taxation rates, criminal punishments, and inheritance law, to give just a few examples.

Historically, then, I think what's interesting is that we can nonetheless speak of a liberalizing period in Middle Eastern history. How to date this age varies wildly. Albert Hourani's Arabic Thought in the Liberal Age dated the period from 1798 (Napoleon's invasion of Egypt, a traditional point of departure for "modern" Middle East history) to 1939.

For myself, I would argue that that the most plausible end date for the "liberal age" of the Middle East would be 1979, which saw: 1. the Soviet Invasion of Afghanistan, 2. the signing of the Camp David Peace between Egypt and Israel, 3. The Islamic Revolution in Iran, 4. the seizure of the Grand Mosque in Saudi Arabia, 5. Saddam Hussein's Presidency of Iraq.

Something like an "age" is a very fuzzy concept. Some of these events demonstrated that the liberal "age" in question had already ended, while others contributed to its antithesis. The region had undoubtedly been already undergoing a period of religious revival, of which the Iranian revolution was one such outcome, but would also, even in Sunni countries, also become a cause.

The mid 20th century Islamic religious revival, as a transnational movement, is an under-studied phenomenon. I don't actually think that I could point to a comprehensive study of it, although I could mention various histories of individual nations during the same period that make clear that it was, in fact, a transnational phenomenon. Though many such images are out of context or ill-informed, photos of women in the 1950s-1970s in countries like Egypt, Iran, or Afghanistan not wearing the veil, in contrast with their 21st century counterparts, are one popular and easily visible example of this phenomenon (if, as I mentioned, potentially an incredibly misleading one given that such photos tended to also have a class basis.)

Though this mid-century Islamic revival very much had as-yet poorly described, decentralized organic roots I would point to two post-1979 developments as having especial importance for your question.

The first is the Saudization of international Islam. As a result of the experience of 1979 and their newly found mass-oil-wealth, Saudi Arabia developed a policy post-1979 of exporting their particular form of Islam--Wahhabism-- which is, compared with most regional customary practices, incredibly "conservative." As a result of Saudi funding, this in effect became the "default" form of Sunni Islam practiced around the world.

Second, and eventually a related issue, was the emergence of Islamist movements as the only viable democratic opposition to status-quo autocracies across the region.

Although he's a comedy writer, the twitter user Karl ReMarx pretty much nails his "simple one-sentence explanation for what caused ISIS".

The failure of the postcolonial elites to create genuine democratic societies and foster a sense of national unity opting instead for military dictatorships that eroded the potential for economic and political development coupled with the historic mistakes of Arab progressive parties and their appeasement towards autocratic rulers contributing to the complete evisceration of alternative political frameworks that could create organic resistance towards external meddling, hegemony and outright military interventions leaving a radical interpretation of religion as the only remaining ideological platform capable of mobilising the disenfranchised exacerbated by the global decline of universal ideals and the rise of identity as a prime mobiliser and enabled by political and financial support from theocratic regimes aiming to shore up their legitimacy and made worse by the collapse of the regional security order creating the conditions for proxy wars and political, social and economic upheaval intensified by geo-politically incoherent international meddling escalating conflicts and leading to a perpetual state of chaos under which the appeal of a revivalist religious-political order embodied by the caliphate becomes attractive particularly when coupled with a millenarian apocalyptic narrative.

To rephrase in a non-ISIS-specific context, the result in almost every country throughout the Middle East was either that the only meaningful opposition to status quo dictators was to be found in Islamist parties, or, in the case for example of Saddam Hussein, that those dictators ultimately embraced a kind of Islamism in an attempt to ride the religious wave.

Anyways, I'm at 9000+ characters and I'm not entirely sure that I've answered your question or even that it is fully answerable, but this seems like a logical enough place to stop. As I said, this will by no means be the last word on this question, so I'm happy to try to take any followups you might have or to point towards additional reading other than the pieces I mentioned above.