When you consider Islam (as a partial answer), your question is not easy to answer in general, but rather should be tackled on a case to case basis, under consideration of many differentiating factors, as wealthy Muslims were obviously seen differently than poor Muslims, scholars different than peasants, influences of certain political factors (during the crusades ect.) should be considered, views might change over time and vary from region to region …
I’ll give you a few starters as a glimpse into the nuanced relationship between Muslims and Christians. In his lovely book about Muslims of Medieval Latin Christendom, Brian A. Carlos notes, that the idea that the Arabic-Islamic and the European-Western-Christian communites were more or less two separate worlds, is obviously wrong. In fact, many Muslims lived in Christian societies, as free subjects, though, during the time. (cf. the introduction). Obviously, religion was not simply religion during the Middle Ages, it defined a person stronger than nationality: “[…] whether he or she was black, white or dark […] a Christian was first and foremost a Christian, and a Muslim, evan if he or she was a native (e.g. naturell) of a Christian realm, was first and foremost a _Sarcenus.” Still, members of all major religions (=Jews, Christians, Muslims) “interacted as tenants and landlords, customers and vendors, debtors and creditors, locals and foreigners, and superiors and subordinates, and often shared agendas with individuals and collectives of other religions that put them in direct an violent conflict with their own agendas.” (pp. 311f.) You’ll find many examples of such interactions throughout the book.
I also want to talk briefly about the relationship between western and Arabic science to demonstrate that an appreciation of Islamic Knowledge could go hand in hand with certain reservations towards Muslim scholars. While Europe wasn't exactly a scientific wasteland during the Middle Ages, it was known, also by contemporaries, that Middle Eastern science was on a much higher level at the time - due to a number of facts such as Islam being a very science friendly religion, their preservation of scientific texts from antiquity which had become practically unknown to the Western World at the time etc. Hence, many of the advances in science were developed in connection with scientific knowledge from the Arabic world and Muslim scholars often enjoyed a high reputation among their kin in Europe. Still, the relation between Arabic/Muslim and European/Christian science has to be seen in a differentiated way.
Consider for example Gerbert of Aurillac, who would later become Pope Sylvester II., and who had travelled to monasteries near Barcelona to study sciences around 970 A.C. It should be noted that neither of these villages were under Islamic Rule at the time. Older sources claim he also went to cities under Muslim rule while he was there, a claim that is disputed by some modern scholars [cf. for example p. 209 in: Celestial Divination and Arabic Science in Twelfth-Century England:The History of Gerbert of Aurillac's Talking Head. In: Journal of the History of Ideas, Volume 73, Number 2, April 2012, pp. 201-222], it is an undisputable fact that he introduced Arabic knowledge into the Western World, such as Arabic Numerals (minus the Zero which only became known after the translation of al-Chwarizmi's Al'jabr (Algebra) ), the abacus and some forms of astrolabia (an astrolabium being an instrument to determine the position of stars and planets at a certain time and place) [cf. the same article, pp. 206f.].
For another example, I would like to present Frederick II of Hohenstaufen, later called Stupor mundi. He grew up in Sicily, and while the stories of him roaming the streets of his hometown and thereby having first intensive contact with Arabic culture are deemed legendary today, his love for Arabic culture cannot be denied. While being excommunicated, Frederick led the sixth crusade and actually conquered Jerusalem – but not by attack, rather, he made a treaty with Malik al-Salih, who allegedly entertained him in his tents for a few months were, even more allegedly, Frederick stated that Allah was a “worthy god”.
Frederick II is often, and righteously so, considered an Arabophile, but his relationship with Islam is very ambiguous. As King of Sicily, he had the Muslim population deported, which would later lead to them being sold into slavery (albeit by a different ruler). On the other hand, “Frederick continued to use Muslim soldiers in his personal bodyguard. And while, Crusading notwithstanding, Frederick certainly engaged positively with Islamic high culture and foreign Muslim elites, his court and his persona were resolutely Christian and Italo-Latin in orientation. Frederic spoke Arabic (as well as Greek), occasionally donned "Saracen" dress, and enjoyed Arabo-Islamic entertainments, such as music and dance. Despite this, unlike the Normans, he was a consumer and translator of, rather than a participant in Arabo-Islamic culture, and like the contemporary Castilian kings, preferred to access it through the medium of Arabized Jews.” [Carlos, p. 91/123] Like Gerbert of Aurillac, Frederick II, the Arabophile (!!!), able to speak and read Arabic (!!!), treasured and learned Arabic/Muslim science, but still preferred to learn it from third hand parties, or mediators if you will and deported Muslims.
Edit: corrected a typo
I just wanted to pop in with a book suggestion, if that's okay (still a bit new here and trying to abide by the rules).
The Ornament of the World (Maria Rosa Menocal, 2009) is a good, accessible study of the culture of tolerance that flourished between Muslims, Jews and Christians in medieval Spain. The author deals with laws about interaction and business practices, social norms and cultural similarities/differences/allowances. She delves quite deeply into the lasting impact on tolerance and collaboration between scholars of the three faiths and the impact it had more broadly on Western European culture. Sometimes she's a bit on the rose-coloured-glasses side of things, and sometimes it gets a bit negative, but it's generally a well-balanced book and a good overview for anyone interested.
I read it ages ago during a Classics course in my undergrad and the impression it left on me is a lasting one. This was ages before my PhD when I was a little history newb and my focus has shifted entirely to Scottish history, but this book is still on my shelf and still something I refer to frequently (or just read for enjoyment!).