Refusing to compromise and falsify identity (5)
I believe the answer is:
rigid
'refusing to compromise' is the definition.
(rigid can mean stubborn or inflexible)
'falsify identity' is the wordplay.
'falsify' becomes 'rig'.
'identity' becomes 'id' (abbreviation).
'rig'+'id'='RIGID'
'and' acts as a link.
(Other definitions for rigid that I've seen before include "Stiff, unbending" , "Incapable of or resistant to bending" , "Not flexible" , "stern" , "Firmly fixed" .)