'non-anaphylactic' is formed from the prefix 'non-' (from Latin 'non', meaning 'not') plus 'anaphylactic' (from the medical noun 'anaphylaxis' derived from Greek elements 'ana-' and 'phylaxis').

'anaphylactic' was derived in modern medical English from 'anaphylaxis' (coined in the early 20th century from Greek roots), and the compound 'non-anaphylactic' arose by adding the negative prefix 'non-' to indicate absence of anaphylactic reaction.

Initially 'anaphylactic' meant 'relating to anaphylaxis'; the compound simply adds negation, so its meaning has remained a direct negation: 'not relating to or causing anaphylaxis.'