'apollinarian' originates from Late Latin, specifically the name 'Apollinaris', which denoted one associated with the Latin name Apollinaris (itself derived from the Greek name 'Apollinaris' related to 'Apollōn' meaning 'Apollo').

'apollinarian' developed in English via Late Latin/Medieval Latin 'Apollinaris' (the name of a 4th-century bishop and later a label for his followers) and came to English as an adjective/noun referring to that person or his doctrine.

Initially it designated someone or something 'of or belonging to Apollinaris' (the person); over time it also came to refer specifically to the theological doctrine (Apollinarianism) and its adherents.