Church only mildly socialist? Answer me! (5,4)
I believe the answer is:
notre dame
'church only' is the definition.
'notre dame' can be an answer for 'church' (I've seen this before). I am unsure of the 'only' bit.
'mildly socialist? answer me' is the wordplay.
'mildly' becomes 'not' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'socialist?' becomes 'red' (red is a kind of socialist).
'answer' becomes 'a' (abbreviation eg in Q and A).
'not'+'red'+'a'+'me'='NOTRE-DAME'
(Other definitions for notre dame that I've seen before include "sacred building" , "sacred place" , "Parisian cathedral" , "Victor Hugo wrote 'The Hunchback of . . . . . . . . .'" , "Parisian landmark" .)