Nonunionized rhymes with:
unionized, unionized, unionized, immunized, unionized, africanized, agonized, aluminized, americanized, antagonized, balkanized, canonized, carbonized, christianized, colonized, demonized, disorganized, galvanized, harmonized, hellenized, homogenized, humanized, immunized, lionized, mechanized, organized, patronized, reorganized, revolutionized, scrutinized, synchronized, unionized, unorganized, urbanized
Nonunionized sounds like:
nagata, nagged, nakata, naked, nast, nasta, nasty, naught, naughty, nauseate, nauseated, necessitate, necessitated, necessity, necked, necktie, negate, negated, negotiate, negotiated, nesseth, nest, nesta, neste, nestea, nested, neustadt, newest, newgate, newgateway, newquist, newscast, newsday, next, nicest, nicety, nicked, niezgoda, night, nikita, niquette, nishida, nist, nixed, njt, noisiest, nonjet, nosed, nuanced, nugett, nugget, nunziata, nunziato, nyquist