Extremely divisive doctrine? Belief in God? (5)
I believe the answer is:
deism
'belief in god?' is the definition.
(I've seen this before)
'extremely divisive doctrine?' is the wordplay.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'doctrine?' becomes 'ism' (suffix for disciplines or schools of thought).
'divisive' with its centre taken out is 'de'.
'de'+'ism'='DEISM'
(Other definitions for deism that I've seen before include "Belief in a god from reason not revelation" , "Belief in a creator" , "Belief in a supreme being who does not intervene in the universe" , "Belief in the existence of God" .)