Republican avoiding skirmish about religion (7)
I believe the answer is:
sikhism
'religion' is the definition.
(I've seen this before)
'republican avoiding skirmish about' is the wordplay.
'republican' becomes 'R' (abbreviation).
'avoiding' suggests deleting specific letters.
'about' indicates anagramming the letters.
'skirmish' with 'r' removed is 'skimish'.
'skimish' anagrammed gives 'SIKHISM'.
(Other definitions for sikhism that I've seen before include "Indian religion founded by Guru Nanak" , "Religion with gurus" , "Kiss him (Anag)" .)