No one knows exactly sure how the evolution of vegetarian zombies occurred, but some suspect that when the person got infected and became a zombie, this person was a vegetarian, so their eating habits carried over.
Barry: I can't believe that zombie didn't eat us!
Lynton: You shouldn't have worried, it's a vegetarian zombie. His diet consists of vegetables, dairy products, and things that aren't meat.
*zombie in the distance* Salad, SALAD!