I’ve read the Crusaders assimilated into the native cultures of the Levant, wearing turbans and jellabiyas while also issuing Arabic coinage. Did they ever form a distinct hybridized culture in their new holdings?
Yes they did, at least according to people back in Europe...although from the crusaders' perspective, it was more of a European microcosm transplanted to the east. In fact I just worked on a similar question last week, so rather than repeat it all here, check out that one for more info and sources:
What was life like as a European living in a crusader state?