'non-dogmatically' is formed in English from the prefix 'non-' (from Latin 'non' meaning 'not') combined with 'dogmatic' (from Greek 'dogma' meaning 'opinion' or 'that which seems true').

'dogma' comes from Greek 'dogma' (from the verb 'dokein' 'to seem, think'), passed into Late Latin and Medieval Latin as 'dogma/dogmaticus', entered English as 'dogmatic'; the productive English prefix 'non-' was added to form 'non-dogmatic', and the adverbial suffix '-ally' created 'non-dogmatically' in modern usage.

Originally 'dogma' meant 'opinion' or 'something that seems true'; 'dogmatic' came to mean 'asserting principles as unquestionably true'; 'non-dogmatically' therefore evolved to mean 'in a way that does not assert rigid, unquestionable principles' and emphasizes openness to other views.