This is actually a really interesting topic, which I wrote part of my undergrad thesis about. I'm going to be leaning heavily on Paul Chevedden's wonderful "The Islamic View and The Christian View of the Crusades: A New Synthesis," which delves deep into primary sources to understand how people at the time actually viewed the Crusades. I will say this is a radical departure from traditional scholarship on the subject - but it's very compelling when you actually dive into it.

You have to think about the timescales. If you look at the world in 621, on the eve of Muslim conquest, most of what we think of as the Muslim world in the Mediterranean is Christian. The Bishops of Aleppo and Hippo are important people. The Levant (modern Syria, Palestine etc.) is a hotbed of Christianity and includes some of the most important Christian sites. Jerusalem is an important Christian city. The Crusades started roughly 400 years later (the traditional date is 1095 - but there are good reasons to think that people in the time would have had different understandings of when the Crusades actually stated). So it had not been such an incredibly long time - scholars in both the Islamic and Christian worlds were concretely aware that the targets of the Crusades used to be important Christian cities. Muslims especially understood the early history of their faith as one of conquest in the name of god, and would have been acutely aware of the fact that they took these lands from Christians. Christians would have been familiar with stories from the bible and the rise of the Catholic Church, when these areas were Christian.

Chevedden argues that when you actually look at the sources, both Islamic and Christians in the times of the Crusades understood them in the same way - a "mirror image" of the Islamic conquest that had taken place several hundred years prior. Both understood them as a Chritian attempt to retake previously Christian lands, in the same vein as the Reconquista and the invasion of Muslim Sicily. It is actually striking the degree to which both Islamic and Christian sources from the 11th century seem in agreement on what Christians are actually doing - partaking in a Mediterranean-wide attempt to retake previously Christian lands from Muslim control. No one at the time would have understood a difference between political and religious motivations - they were tied together, and both involved. But both Christians and Muslims understood the endeavour in the same way, and in the context of these areas having been Christian comparatively recently.

This doesn't mean, obviously, that Muslims liked it. They believed that that were spreading and maintaining the true faith - and saw Franks as being comparatively barbarous. They thought that losing these lands would not only be a failure of faith, but also a political step backwards, and a step backwards in civilization - much like Rome would have seen an invasion by the Huns.

A really interesting read on this topic is Ussama ibn Munqidh's "Kitab al-I'tibar" ("Book of Learning by Example). Munqidh was born in 1095 and lived until 1188, so had a front-row seat to a huge part of the Crusader Era. He wrote his book as a memoir and instructional volume using his life experience as material. He has some very interesting passages concerning the Franks - he sees Franks that have been there for a generation as basically being equals of their Islamic peers - genteel, educated, etc. EDIT: I wrote this quickly and that's porbably a mis-characterization. He saw Franks who had been in the Levant longer as being more civilized and more similar to local Muslims, not equals. But new Franks incoming he sees as barbarians who are barely human. He draws a lot of parallels between himself and his adversaries as he fights them - he recognizes some of the same merits in them that he sees in his brethren, and seems to implicitly understand himself as part of a struggle between to righteous groups both fighting for god as they see it. Which, again, is not to say that he thinks the Franks are right - just that he understand where they're coming from. He does usually follow mentions of the Franks with some call for Allah to smite them or curse them, but this was also a bit of a literary convention. He did strike up close friendships with Franks from time to time as well.

He does, however, roundly ridicule Frankish institutions. One of the best examples is the use of "trials" to prove innocence - in one case, they conducted a trial by water and he describes the man as trying desperately to sink to prove his innocence.

EDIT: Corrected the title of ibn Munqidh's work from the translated title of the edition I read to the actual title as written by ibn Munqidh.