'anti-theistically' originates from modern English, formed from the prefix 'anti-' (from Greek 'anti' meaning 'against') + the adjective 'theistic' (from 'theism', ultimately from Greek 'theos' meaning 'god') with the adverbial suffix '-ally' (-> '-ally' -> '-ically'/'-istically' in formation).

'anti-' was borrowed from Greek 'anti' into English via Latin/French; 'theism' comes from Greek 'theos' + suffix '-ism' and entered English via Medieval/Modern usage; 'theistic' was formed from 'theism' + '-ic' and then combined with 'anti-' to form 'anti-theistic', to which the adverbial ending '-ally'/'-ically' produced 'anti-theistically'.

Initially formed to mean 'against theism' and, over time, retained this primary sense; its use as an adverb simply denotes performing or expressing that opposition.