No, in most cases it was actually worn by the Catholic Ghegs but also the Muslim Ghegs. It was worn over the Qeleshe/Plis
So what, Crusaders wore them aswell. You don't see Arabs in Central or Northern Europe wearing them.
https://www.ecomodelismo.com/ECO_img...ROME-90014.jpg
http://en.spbsouvenir.ru/d/740660/d/...II_Century.jpg