late 14c., "not in conformity with Church rules," from Old French irreguler "irregular, incapable, incompetent" (13c., Modern French irrégulier), from Medieval Latin irregularis "not regular," from assimilated form of in- "not, opposite of" (see in- (1)) + Latin regularis "having rules" (see regular (adj.)). General sense of "not conforming to regular rules or principles" is from late 15c. "It expresses the fact of being out of conformity with rule, but implies nothing more with certainty. Yet the word is sometimes used in a sinister sense, as though it were a euphemism for something worse." [Century Dictionary] Meaning "unsymmetrical" is from 1580s. In reference to variable stars, from 1797.
"one not belonging to a regular body" of any sort, "one not subject to or not conforming with established regulations," 1610s, from irregular (adj.). Main modern sense of "a soldier not of the regular army" is from 1747.
Doubtless, the life of an Irregular is hard; but the interests of the Greater Number require that it shall be hard. If a man with a triangular front and a polygonal back were allowed to exist and to propagate a still more Irregular posterity, what would become of the arts of life? Are the houses and doors and churches in Flatland to be altered in order to accommodate such monsters? [Edwin Abbot, "Flatland: A Romance of Many Dimensions," 1885]