"of or pertaining to the Pope or the Roman Catholic Church," 1520s, a hostile coinage from Pope + -ish.
Entries linking to popish
pope n.
"the Bishop of Rome as head of the Roman Catholic Church," c. 1200, from Old English papa (9c.), from Church Latin papa "bishop, pope" (in classical Latin, "tutor"), from Greek papas "patriarch, bishop," originally "father" (see papa).
Applied to bishops of Asia Minor and taken as a title by the Bishop of Alexandria c. 250. In the Western Church, applied especially to the Bishop of Rome since the time of Leo the Great (440-461), the first great asserter of its privileges, and claimed exclusively by them from 1073 (usually in English with a capital P-). Popemobile, his car, is from 1979. Pope's nose for "fleshy part of the tail of a bird" is by 1895. Papal, papacy, later acquisitions in English, preserve the original vowel.
-ish
adjectival word-forming element, Old English -isc "of the nativity or country of," in later use "of the nature or character of," from Proto-Germanic suffix *-iska- (cognates: Old Saxon -isk, Old Frisian -sk, Old Norse -iskr, Swedish and Danish -sk, Dutch -sch, Old High German -isc, German -isch, Gothic -isks), cognate with Greek diminutive suffix -iskos. In its oldest forms with altered stem vowel (French, Welsh). The Germanic suffix was borrowed into Italian and Spanish (-esco) and French (-esque). Colloquially attached to hours to denote approximation, 1916.
The -ish in verbs (abolish, establish, finish, punish, etc.) is a mere terminal relic from the Old French present participle.