Couple that are not straight about male’s forbidden love (6)
I believe the answer is:
bigamy
'forbidden love' is the definition.
(crime of marrying more than one person)
'couple that are not straight about male's' is the wordplay.
'couple' becomes 'bi' (I am not sure about this - if you are sure you should believe this answer much more).
'that are not straight' becomes 'gay' (straight is the opposite of gay).
'about' is an insertion indicator.
'male' becomes 'm' (common abbreviation).
'gay' placed around 'm' is 'gamy'.
'bi'+'gamy'='BIGAMY'
(Other definitions for bigamy that I've seen before include "Crime involving two better halves!" , "In law, having two spouses at the same time" , "Crime of double marriage" , "overmatiness" , "Matrimonial crime" .)