a prefix used freely in English and meaning "not, lack of," or "sham," giving a negative sense to any word, 14c., from Anglo-French noun-, from Old French non-, from Latin non "not, by no means, not at all, not a," from Old Latin noenum "not one" (*ne oinom, from PIE root *ne- "not" + PIE root *oi-no- "one, unique"). In some cases perhaps from Middle English non "not" (adj.), from Old English nan (see not). "It differs from un- in that it denotes mere negation or absence of the thing or quality, while un- often denotes the opposite of the thing or quality" [Century Dictionary].
1640s, "belonging or pertaining to a schismatic sect," applied by Presbyterians to Independents, from Medieval Latin sectarius, from secta "religious group, sect in philosophy or religion" (see sect). By 1796 as "of or pertaining to sects or to attachment to a particular sect; including the tenets of a sect," hence "bigotedly attached to a sect." Sectarial (1816) is "Chiefly used with reference to Indian religions" [OED].
As a noun, "one of a sect" (1650s), especially "one who attaches excessive importance to a sect." The older word in this sense is sectary.
<a href="https://www.etymonline.com/word/non-sectarian">Etymology of non-sectarian by etymonline</a>
Harper, D. (n.d.). Etymology of non-sectarian. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/non-sectarian