The most common and most likely answer to this crossword clue is the 9 letter word DIRTINESS
I've seen this crossword clue in The Times
D
I
R
T
I
N
E
S
S
More clues leading to the result DIRTINESS
Buddy explains!

The straight part
We know that "Being obscene" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case being obscene = dirtiness.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.