After Saladin had purified the Dome of the Rock following his conquest of Jerusalem, he had inscribed within it the following: "Saladin has purified this sacred house from the polytheists." Did Medieval NE Muslims view Christians as polytheists or was that a blanket term applied to all non-Muslims?

Yes, Muslims in the Near East (and in Spain) often described Christians this way.

As u/Al_Mamluk noted, the story goes that Frederick II visited the Dome of the Rock in 1229, after the sultan of Egypt al-Kamil made a treaty with Frederick and agreed to return Jerusalem to him. According to Sibt ibn al-Jawzi:

“…the Emperor looked at the inscription that runs round the inside of the sanctuary, saying: ‘Saladin purified this city of Jerusalem of the polytheists....’ and asked: ‘Who would these polytheists be?’” (Gabrieli, pg, 162)

Ibn al-Jawzi is translated in Gabrieli’s Arab Historians of the Crusades, although as Al_Mamluk mentioned it’s also in Maalouf’s Crusades Through Arab Eyes. Maalouf notes that Frederick was obviously being sarcastic, and based on this and Frederick’s other statements/actions, Ibn al-Jawzi was suspicious that Frederick was neither Christian nor Muslim, but possibly an atheist. I’m not sure if the inscription is still there or not.

Frederick’s question was ironic, but yours is not, so: why did Muslims think Christians were polytheists? There were still Christian communities in the Near East, but Muslim rulers paid little attention to them and weren’t very interested in the intricacies of Christian doctrine. They were even less interested in the far-away Christians in Europe. I wrote a little bit about this in a previous question last year:

What stereotypes or preconceptions did the Arab world hold about Europeans during the Medieval era?

Christians were typically described as “People of the Book” (ahl al-Kitab), since they’re mentioned in the Qur’an and Muslims were supposed to welcome and protect them. The other People of the Book were Jews and Zoroastrians, but all of the ahl al-Kitab were also often simply described as “unbelievers” (kafirun). Christians specifically, but not Jews, were sometimes called “polytheists” (mushrikun). A mushrik is someone who commits shirk, literally “association”, i.e. associating other beings with the one true God.

“…the Franks are called ‘polytheists’ (mushrikun) and the ‘enemies of God’. Sibt b. al-Jawzi labels them ‘people of stubbornness’ whilst Ibn al-Dawadari derides them as ‘worshippers of crosses’. They are also described as ‘the people of the Trinity’ (ahl al-tathlith), ‘the servants of the Messiah’, and ‘polytheist dogs’.” (Hillenbrand, pg. 303-304)

As far as Muslims could tell, Christians worshipped Jesus, the Holy Spirit, Mary, and innumerable saints alongside God. They were especially offended by the concept of the Trinity, which seemed to imply that Christians believed in three gods. It was as plain as day, Christians were polytheists.

Of course, this worked both ways, since the native Christians of the Near East and European Christians also had little or no idea what Islam was really all about. I answered a question about this last year as well:

I'm a Crusader heading towards the Holy Land in 1096. How much do I understand about Islam?

Muslim accounts of the crusades frequently call European crusaders polytheists, but European accounts always call the Muslims polytheists as well. Christians didn’t quite know what to make of Islam; it wasn’t Judaism, so was it a heretical form of Christianity? If it wasn’t Christianity or Judaism, then it must be the only other form of religion they knew about, polytheistic paganism. It’s interesting to note, though, that Muslims concluded that Christians were polytheists based on Christianity’s own doctrines, while Christians believed Muslims were polytheists based on...nothing.

Sources:

Francesco Gabrieli, Arab Historians of the Crusades, trans. E. J. Costello (University of California Press, 1969)

Carole Hillenbrand, The Crusades: Islamic Perspectives (Routledge, 1999)

Amin Maalouf, The Crusades Through Arab Eyes (Schocken Books, 1984)