"one who changes from one sect, creed, etc. to another," late 14c., proselite, "a convert, especially "a heathen convert to Judaism" (in Biblical writings, e.g. Matthew xxiii.15, Ezekiel xiv.7), from Old French proselite (13c., Modern French prosélyte), from Late Latin proselytus, from Greek prosēlytos "convert (to Judaism), stranger," literally "one who has come over."
It is a noun use of an adjective meaning "having arrived," from pros "from, forth, toward" (see pros-) + eleusomai "to go, come" (from PIE *elu-to-, from root *leudh- "to grow up, come out" (see liberal (adj.)).
word-forming element making nouns implying a practice, system, doctrine, etc., from French -isme or directly from Latin -isma, -ismus (source also of Italian, Spanish -ismo, Dutch, German -ismus), from Greek -ismos, noun ending signifying the practice or teaching of a thing, from the stem of verbs in -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached. For distinction of use, see -ity. The related Greek suffix -isma(t)- affects some forms.
<a href="https://www.etymonline.com/word/proselytism">Etymology of proselytism by etymonline</a>
Harper, D. (n.d.). Etymology of proselytism. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/proselytism