Heathen, not half rude about sources of faith and immortality (7)
I believe the answer is:
infidel
'heathen' is the definition.
('infidel' can be a synonym of 'heathen')
I don't understand the remainder of the clue.
(Other definitions for infidel that I've seen before include "Unbeliever" , "Person who does not believe in a religion" , "Person who has no faith, or the wrong one" , "One who doesn't believe" , "Someone who does not acknowledge your god" .)