before vowels hagi-, word-forming element meaning "of a saint, saintly, holy," from Greek hagios "sacred, devoted to the gods" (of things), "holy, pure" (of persons), in Ecclesiastical Greek, "a saint," which is perhaps from PIE *yag- "to worship, reverence" (source also of Greek agnos "chaste," Sanskrit yajati "reveres (a god) with sacrifices, worships," Old Persian ayadana "temple").
word-forming element meaning "worship of," used as an element in native formations from 19c. (such as bardolatry), from Greek -latreia "worship, service paid to the gods, hired labor," related to latron (n.) "pay, hire," latris "servant, worshipper," from PIE *le- (1) "to get" (see larceny).
<a href="https://www.etymonline.com/word/hagiolatry">Etymology of hagiolatry by etymonline</a>
Harper, D. (n.d.). Etymology of hagiolatry. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/hagiolatry