Put off man avoiding cleansing product (5)
I believe the answer is:
deter
'put off' is the definition.
(both can mean to discourage)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for deter that I've seen before include "Discourage (an activity)" , "Daunt" , "Try to prevent" , "Prevent by instilling fear" , "Check" .)