I am not that familiar with the Wattasids and Saadians of Morocco, but I can talk a little about the Ottomans. The most important thing to keep in mind is that in the 16th and 17th centuries, the Ottoman Empire is not some separate "Islamic world" off to the southeast. It is a major player in European politics and warfare.

In spring of 1529, a group of gospel-minded German princes is drawing up the document of protest that will ultimately yield their ideology the label Protestant. At the same time, an Ottoman army is preparing to march on Vienna. Their mutual target? The Hapsburg Holy Roman Empire.

While Ottoman and Western navies fought for control of various Mediterranean islands, coastlines and shipping routes (the famous Battle of Lepanto is 1571), the Hungarian frontier was the front line for Ottoman ambition in Europe. Due to the decentralized nature of the HRE, that meant the Habsburgs were their primary target. At the dawn of the Reformation, the Habsburgs under Charles V pretty much directly controlled Austria, Spain and some of the Netherlands. This political situation shapes the Ottoman reaction to the Reformation.

To be clear, the German Protestants made no attempt to endear themselves to the Ottomans. In 1528, Luther himself published a treatise "On the War Against the Turks," in which he gave up on the idea of converting Muslims to Christianity and focused instead on defending Western Europe from the Turks. And indeed, it was to Catholic France--sworn enemies of the very Catholic Habsburgs--to whom the Ottomans reached out first.

This decision benefited everyone except Charles. As rumors of a true Franco-OE alliance (which may or may not have resulted from their diplomatic efforts) helped distract some Hapsburg attention, Lutheranism in German gained a lasting foothold. When Protestant princes took up arms against Catholic in the Schmalkaldic Wars, the Ottomans got to take a necessary breather. (Since the Protestants actually lost the SW wars, the HRE's Ottoman-aided weakness that allowed them to gain a foothold ended up being crucial for Prot's long-term success: a minor Prot. victory after the initial peace treaty forced the eventual Peace of Augsburg, establishing that the religion of an HRE territory would be the religion of its prince, so long as that religion was Lutheranism or Catholicism.

Around this time, the Ottomans made diplomatic inroads with other enemies of the Habsburgs, namely Protestants in Elizabethan England and Calvinists in the Netherlands. Letter exchanges reveal a diplomatic emphasis on religious mutual ground, especially a common rejection of "idols" (Catholic veneration of images). This is diplomacy, not a real effort at interreligious dialogue--the periods of Byzantine iconoclasm centuries of earlier had dont nothing to endear Christianity and Islam. Instead, the diplomacy opened the door to an Ottoman-Dutch alliance that, again, aided both parties tremendously.

Initially, of course, Ottoman promises of aid to Dutch Protestants were mostly lip service, and a few waves of the Dutch Revolt failed. But the ongoing skirmishes between Spain and the OE diverted Iberian resources away from the Low Countries, eventually allowed the 1570s wave of rebellion to stick its landing. For their part, the Ottomans gained crucial diplomatic and trade ties with a rising world power.

Transylvanian Hungary hosted the only sizable Western Christian population under Muslim control. Here, the Ottomans extended their recognition of (Catholic) Christians as dhimmis or people of the book to Protestants as well. As the Reformation in Hungary tinged Calvinist, the Ottomans proved great supporters of that church in their territory, again seeing it as a weapon against Habsburg Vienna. They were also happy to continue extending the same status to Catholics. Refugees of inter-Christian conflict as well as problems within a branch of Christianity or even a specific Catholic order all took shelter in Ottoman territory. And under the crescent, which permitted religious practices but not religious construction by non-Muslims, diverse Christian populations across the OE ended up rotating holy services in the same church buildings.

So overall, this is a political story much more than a religious one. The diplomatic ties tentatively established through initial epistolary diplomacy and eventual ambassadorships did not prove completely reliable under duress. Nevertheless, Western and Eastern parties alike--Protestant, Muslim, and sometimes even Catholic--found it useful to keep the possibility of alliance alive.

God save the king (and his useful army), they could all agree, as long as that king was not also Emperor.