Right-winger supporting obscurity, not rocking the boat (10)
I believe the answer is:
conformist
'not rocking the boat' is the definition.
(conforming is doing the same as everybody else)
'right-winger supporting obscurity' is the wordplay.
'right winger' becomes 'con' (conservative).
'supporting' becomes 'for' (being for something means supporting it).
'obscurity' becomes 'mist'.
'con'+'for'+'mist'='CONFORMIST'
(Other definitions for conformist that I've seen before include "Tending to comply with social norms" , "Person who toes the line" , "One complying with accepted practices" .)