Insensitive Conservative: right idiot (5)
I believe the answer is:
crass
'insensitive' is the definition.
(a crass comment might be insensitive)
'conservative right idiot' is the wordplay.
'conservative' becomes 'C' (UK political abbreviation).
'right' becomes 'r' (abbreviation).
'idiot' becomes 'ass' (both can mean a stupid person).
'c'+'r'+'ass'='CRASS'
(Other definitions for crass that I've seen before include "Blundering" , "Grossly insensitive" , "Unrefined" , "Witless" , "'Gross, vulgar (5)'" .)