Are interstellar conflicts possible or probable?
If there are no other technological civilizations, then they are impossible.
If there is no FTL, then they are improbable.
If there is no FTL and if technological civilizations are rare, then they are improbable verging on impossible.
What would there be to fight about over such distances?
The Ai Chun in Poul Anderson's World Without Stars and the Aleriona in his The Star Fox have very old static cultures and are genetically incapable of tolerating engulfment by a younger, dynamic species. The Alori in Anderson's The Peregrine have an organically based culture that cannot tolerate engulfment by a mechanically oriented civilization. The Merseian Roidhunate in Anderson's Technic History is racially supremacist and cannot tolerate any species that remain independent of it.
In James Blish's future histories, there are mainly imperialistic relationships between interstellar civilizations. In one branch of his Haertel Scholium:
Adolph Haertel discovers antigravity and flies a tree hut to Mars;
Mars is colonized;
Garrard makes the first successful interstellar round trip with the Haertel overdrive;
Arpe replaces the Haertel drive with the Arpe drive and experiences microcosmic telepathy;
using a third interstellar drive, the Standing Wave, the forces of the Terrestrial Matriarchy encounter an outpost of the telepathic Central Empire.
Thus, an interstellar conflict begins at the end of a future historical sequence. Species that think with ganglia instead of with brains detect the weak parapsychological forces and unite telepathically, regarding brained beings as insane, so that conflict is inevitable.