Hybrid between these two different species and diet?

Let's say that there are two different animals, Species A and Species B, and they are closely related enough to each other to mate and produce hybrid offspring. Both species are omnivores, and while Species A preys on Species B, Species B never eats Species A. If a pair of those two species were to mate and produce hybrid offspring, then would the hybrids be likely to eat Species B? If it did, then would that make them "half-cannibal"? Would Species A be inclined to eat the hybrids, and would that make them "half-cannibal"?