'anti-mediaeval' is formed in modern English by combining the prefix 'anti-' (from Greek 'anti', meaning 'against') with 'mediaeval' (an older spelling of 'medieval').

'mediaeval' comes from Medieval Latin 'mediaevus' (from Latin 'medium aevum' meaning 'middle age'); the modern spelling 'medieval' became common later, and English formed compounds such as 'anti-mediaeval' by adding the prefix 'anti-'.

Originally, 'mediaeval'/'medieval' described something 'of the Middle Ages'; with the addition of 'anti-' the compound came to mean 'against or hostile to medieval ideas or revivalism'.