A majority of observers interviewed see the Middle East as unstable at present but
that it will, or could, become less volatile in the future.
Option Elimination -
(A) that it will, or could, - We need that after the first verb to maintain parallelism. Or it would be better to have a verb after "but" and before the beginning of the relative clause.
(B) that it would, or could, - We need that after the first verb to maintain parallelism. Or it would be better to have a verb after "but" and before the beginning of the relative clause. Moreover, this is not a conditional or hypothetical situation. So, the use of would is wrong.
(C) it will be or could - We need another verb after but some equivalent of see. Otherwise, how can they see it as unstable and less volatile simultaneously? D communicates that very well with the contrast. They see it as unstable but believe it will be or could become less volatile.
(D) believe that it will be or could - perfect. "it will be less volatile in the future" or "could become less volatile in the future."
(E) think the Middle East would or could - "would" conditional can be used with past "thought," but here we have present "think." So we need a simple future "will be."