'anti-materialistically' is formed in modern English by adding the adverbial suffix '-ly' to the adjective 'anti-materialistic', itself built from the prefix 'anti-' + 'materialistic'.

'anti-' comes from Greek 'anti-' meaning 'against'; 'materialistic' derives from 'materialism' + the adjectival suffix '-istic'; 'materialism' comes from Latin 'materia' (meaning 'matter, material') via French/Latin developments.

Initially, elements like 'anti-' and 'material-' meant 'against' and 'matter' respectively; over time the compounded adjective/adverb came to mean 'in opposition to valuing material possessions', which is the current specific sense.