The most common and most likely answer to this crossword clue is the 7 letter word FOULEST
I've seen this crossword clue in The Daily Telegraph
F
O
U
L
E
S
T
More clues leading to the result FOULEST
Buddy explains!

The straight part
We know that "Most obscene" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most obscene = foulest.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 FOULEST mean?
FOULEST adjective- Covered with, or containing unclean matter; dirty.
- (of words or a way of speaking) obscene, vulgar or abusive.
- Detestable, unpleasant, loathsome.
- Disgusting, repulsive; causing disgust.
- Ugly; homely; poor.
- (of the weather) Unpleasant, stormy or rainy.
- Dishonest or not conforming to the established rules and customs of a game, conflict, test, etc.
- Entangled and therefore restricting free movement, not clear.
- Outside of the base lines; in foul territory.