Non-believer eat this rubbish? (7)
I believe the answer is:
atheist
'non-believer' is the definition.
(I've seen this before)
'eat this rubbish?' is the wordplay.
'rubbish?' indicates anagramming the letters (a poor quality or rubbish spelling of the letters).
'eat'+'this'='eatthis'
'eatthis' with letters rearranged gives 'ATHEIST'.
(Other definitions for atheist that I've seen before include "Disbeliever in deities" , "One disbelieving in the existence of God or gods" , "One who believes there is no god" , "I don't believe" , "One who disbelieves the existence of gods" .)