The most common and most likely answer to this crossword clue is the 8 plus 8 letter word PHONETIC ALPHABET
I've seen this crossword clue in The Times
P
H
O
N
E
T
I
C
A
L
P
H
A
B
E
T
Buddy explains!
The straight part
We know that "Words for letters that keep Romeo and Juliet apart" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case words for letters that keep romeo and juliet apart = phonetic alphabet.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.