Exactly so. I would not expect to see educated Islamic troops or armies to eschew armor. And certainly, not all sects believe the same thing. That said, the “village meathead” type of terr who’s been brainwashed in a madrassa since birth and has never been to the West is not likely to purchase or request armor, preferring to place trust in “in’sh’Allah.”
You are wrong about the armor issue, though. With the introduction of heavy plate armor, crossbows became obsolete against heavy Western cavalry. Plate armor was *tested* and “proofed” using crossbows with AP quarrels at point blank range.
Yes, eventually armor progressed technically by the end of the crusades and after that, but the Pope had still stated what he earlier stated during the start of the crusades. Islam did not use the crossbow much. The Western world had Knights while the eastern world had Cataphracts. During the early to mid crusades the Cataphract armor was superior to that of the Knights Templar and the Knights Hospitalier. Just look at any drawing of those Knights and compare it to any drawing of the Cataphracts from that time period. The Eastern world had more advanced armor during that time because Islam had conquered and assimilated a more advanced Eastern Rome as compared to the Germanic tribes which had conquered a less advanced Western Rome. While the Germanic tribes assimilated Rome earlier, it took hundreds of years to advance out of the dark ages by converting to Christianity. The Middle East also adopted the military advances of the far east at that time, before Western Europe (gunpowder for example). Eventually however the Mongols arrived and made the heavily armored knights and cataphracts relatively worthless. Even with their most advanced armor.