Because they hold that animals have a soul and we kill them, whereas plants have no soul, so it is permitted to eat them. A materialist would not distinguish between them; for him, a plant and an animal are the same thing.

Factually, that is certainly not correct. What you mean to ask is whether vegetarianism is compatible with materialism, on the conceptual level. Before you ask me that, ask me whether morality is compatible with it.
See my discussion of this in the fourth notebook.
Though specifically regarding vegetarianism, one can think of an explanation, but it depends on the reason for the vegetarianism. If it is because animals are abused, there is no need to assume that they have a soul. People simply do not want to cause pain. If they see value in the lives of animals, that is something else.

I think the Rabbi means the fourth notebook, not the fifth.

Indeed, correct. I got confused.