The most common and most likely answer to this crossword clue is the 6 letter word COARSE
I've seen this crossword clue in The Daily Telegraph
C
O
A
R
S
E
More clues leading to the result COARSE
- Not refined, bringing rowing gear into Church
- Rows in church, so rude
- Some food said to be lacking taste
- Rough path, we hear
- Broadcast programme of inferior quality
- Inferior, so joint bottom?
- Rough characters appear when Atletico and Arsenal meet
- Unrefined programme reported
- Firm buttocks of low quality
- Firm bum? That’s crude!
Buddy explains!

The straight part
We know that "Obscene" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obscene = coarse.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.
What does COARSE mean?
COARSE adjective- Composed of large parts or particles; of inferior quality or appearance; not fine in material or close in texture.
- Lacking refinement, taste or delicacy.