Continuing the discussion, Noah Millman offers an interesting alternative counterfactual:

Imagine, if you will, that the Third Crusade was a smashing success. Richard Lionheart wins a huge and surprising victory over Saladin and recaptures Jerusalem. Saladin’s dominion splinters, and the Saracens are unable to make a renewed assault on the Kingdom of Jerusalem. Instead, an Anglo-French Catholic island survives for twelve generations, succumbing only in the 15th century to the Ottoman assault.

After the Ottoman conquest, the Angevins, as they come to call themselves, scatter across the empire, settling primarily in Syria, Egypt and western Anatolia. There is a brief flurry of enthusiasm for the restoration of their lost kingdom at the time of the Greek revolt, and while it comes to nothing at the time, over the course of the 19th century there is a steady migration of Angevins, promoted by Catholic knightly orders, back to the Levant. Dreams of restoration do not become a reality until after World War I. In the wake of Turkish massacres of Angevins, Britain demanded the League of Nations restore the Kingdom of Jerusalem under British protection. In spite of protests from the Sharif of Mecca, the French government, and the World Zionist Congress, the proposal was accepted and the Kingdom of Jerusalem, stretching from Tyre in the north to Jerusalem in the south, was restored in 1922.

I’ll pass briefly over the next 70-80 years of history – riots by the Samarian Arabs in the 1930s; occupation by, resistance to and collaboration with the Axis; the lopsided victory in the Suez War and its complex aftermath; the abdication and the ascendancy of the Protector . . . By the end of the 20th century, the erstwhile Kingdom of Jerusalem is locked in a seemly endless conflict with the Samarian Arabs. Back when it was a bulwark against Soviet influence, the Angevin state was a logical ally of the United States. But now, realist critics of the Angevin-American alliance argue that it is a millstone around America’s neck – an unnecessary embarrassment and a cause of friction between America and the far more important Gulf oil states. And yet, as the Angevin position gets more and more difficult, America binds herself ever more strongly to her odd little ally.

Why should that be? Obviously, for reasons of affinity. And yet, that affinity itself needs a bit of unpacking. The Angevins speak a different language (Norman French), and have a wildly different culture. They were never a colony of the United States. The traditional Catholicism that predominates in the Kingdom is a relative rarity in America, where most Catholics are tied to the faith by ethnic identity as much as anything. America’s Jews for obvious reasons have always resented the existence of the Angevin state, and the Irish, in spite of a common religion, have never warmed to what many of them see as a relic of British imperialism, medieval and modern. It’s really only among a slice of the American elite – old-line Anglophilic WASPs and traditionalist Catholics – that the affinity is profound. But as these segments are overrepresented in the elite relative to their percentage of the American population, their affinity has an outsized impact on American policy and, as well, on national perceptions.

This is a very imaginative alternative history, but my guess would be that there would not be an especially strong American affinity for this Angevin state. As the successor of the actual Crusader states, the Angevins would be regarded by most Americans as embodying the worst of the Old World, and in the latter half of the 20th century their traditional Catholicism would not inspire feelings of affinity and identification outside of a very small number of Catholics here. On the contrary, as with most Christians in the East, they would appear to most Americans to be very foreign and unlike “us.” It is typical that Americans know little and care less about Near Eastern Christians, including the Catholic communities who still live in the region right now, and where evangelical Protestants see Israel as the fulfillment of God’s promise and the continuation of the covenant they would see a restored Angevin kingdom as something of a usurper in the Holy Land and, in their most extreme Hagee-like expressions, as a forerunner of Antichrist.

Coming back to the original description Noah provides, it is improbable that the Ottomans would have harmed Catholic subjects en masse during this counterfactual WWI, seeing as how they did not touch them during the actual war. Ottoman massacres of Christian populations were primarily limited to members of the Greek and Armenian millets (as well as the Assyrians of Anatolia and Iraq), because these communities were either under the protection of Allied powers or were seen as sympathetic to the cause of the Allies, while attacks on Catholics, even Francophone descendants of the Crusaders, would have harmed relations with Austria. Therefore, it would be unlikely that the Angevins would have suffered the sort of persecution that would give their cause automatic sympathy, and so there would not be the sort of awareness about their plight or their history in the American public as there was about the Armenians or the Greek refugees from Anatolia. It is equally unlikely that the Third Republic, which in reality did take Mandate Syria and Lebanon partly because of the Catholic populations dwelling there, would not want to have some control over the new Angevin territory as well.

Had it been a French-run Mandate territory, it is not hard to imagine how the kingdom, like other French territories in the Mediterranean, would have come under control of the Vichy and given their background the Angevins might have been quite ideologically inclined to support the Vichy regime. As such, the state probably would have suffered the taint of collaboration, but unlike in Greece there would be no exiled monarchy to restore in place of the collaborators, and unlike in Greece there probably would not have been a broad resistance movement led by communists. Instead, the monarchy of the Jerusalemite kingdom would have been abolished, and a left-leaning secular republic would have been established in its place, and the anticommunist political right in the Angevin state would be tarred with collaboration for a long time after the war. Once independent after WWII, it is not hard to imagine how this Jerusalemite republic then becomes part of the Non-Aligned Movement and its conflicts with neighboring Arabs become mostly a regional concern, rather than a global one that involves the superpowers.