Schools run by, or under the auspices of, mainstream churches were once the mainstay of conservative values in many Western countries. The schoolmasters and schoolmistresses of times past were natural conservatives, valuing hierarchies of authority, almost military (or monastic?) routine, and a relatively stable body of cultural lore to be passed on - Christian texts, Greek and Roman texts, and various literary works in English and European languages.
In many ways this traditional amalgam of Greek, Roman and Christian ideas became a liability for the West because of the high prestige accorded to classical learning and literature, and the low status attached to science and technology. Nietzsche, steeped in the classical tradition, saw science as democratic and levelling. At the school I attended from the age of nine to the age of seventeen - an institution which carried the Middle Ages well into the second half of the 20th century - Latin and French were high-prestige subjects and, before some long-overdue renovations, our chemistry laboratory would have made any time-travelling alchemists feel right at home.
But there is no doubt that the West's shared cultural traditions helped to create a sense of social harmony at home and the sense of belonging to a wider world; that the widespread teaching and learning of Latin and Greek helped to create self-discipline and a sense of history; and that the tedium of regular services in the school chapel taught the invaluable but dying art of sitting still.