You agree that the Crusades were motivated by religion. Does that mean you, personally, think the Bible justifies them (i.e. that true Christianity should include crusades)? I think those are two separate questions.
The issue here is that there are many interpretations of religions. The Quran's writings on sex with slaves are somewhat contradictory, but can certainly be used to justify sexual slavery if you are motivated to do so. And indeed, there are examples of sexual slavery in the world today that is explicitly justified on religious Islamic grounds. Boko Haram and Isis for example.
I think you can argue, quite persuasively, that the Quran doesn't in fact justify rape gangs. But I don't think you can say that because of that the men's religious beliefs were not relevant.
These were not men who were piously trying to do their religious duty. But, from the reporting I've read, including court reporting, it seems that their view of non-Muslim women as inferior was in fact in many cases part of that horrible mix. And there is plenty of support in the Quran, sadly, for treating non-Muslims harshly (and, certainly, plenty of support for more enlightened views too).