Omg it’s so delightful that I get to share this, because I was literally just looking for books on the same topic!! Let me put a couple down that I have found and describe them to you :) Robert Bartlett’s “The Making of Europe” is a fat tome that I’m currently struggling through. It covers the crusades as part of a broader history of colonialism in the mid-late medieval/feudal period. Not exclusively about the crusades in Muslim lands (i.e. in Palestine, Syria, and the Iberian peninsula), also talks about the Baltic crusades and colonization in Greek territories. Super interesting, super dense, covers a lot of stuff other than the crusades, but definitely talks about social and cultural beliefs.

“The Expansion of Latin Europe: the Eastern Mediterranean Frontier” is a collection of essays I haven’t had the chance to crack into yet, but definitely covers a lot of what you might be looking for, and is much more organized into short chapters so you could probably select more easily. Haven’t read it though.

Finally, “crusading and the crusader states” by andrew jotischky has some sections that talk about things like absolution through crusading and views of Muslims; but it’s scattered throughout rather than in one section. From what I’ve read of it (not much) I think in terms of a comprehensive history that talks about sociocultural aspects of the crusades specifically, this one is the one I would recommend the most. Hope one of these sounds interesting or helps you find something else :)