I was wondering if there has ever been a group of Knights that has never fit into the Chivalrous type of knighthood. I understand that the Teutonic, Templar and Hospitalier knights were all of Catholic origins, but has there ever been a non-religious order of knights?
What do you mean by the 'Chivalrous' type of knighthood?
Knightly or chivalric orders do exist outside those you've mentioned, such as the Order of the Garter (England), Order of the Golden Fleece (Burgundy), Company of the Star (France) but they proliferated from the fourteenth-century onwards and will all have some Christianised ritual aspects even if their purpose is secular.