Odd characters in cult ain't family! (4)
I believe the answer is:
clan
'family' is the definition.
(I know that clan is a type of family)
'odd characters in cult ain't' is the wordplay.
'odd characters in' means one should take alternating letters (the letters at odd-numbered positions).
'cult'+'aint'='cultaint'
The alternate letters of 'cultaint' are 'CLAN'.
(Other definitions for clan that I've seen before include "Tribal family" , "Group with a tartan?" , "Macdonald, perhaps" , "Group of related families" , "Tribe or collection of families under a cheiftain" .)