Interesting. But the dictionary definitions above are purely descriptions of the meaning of have as eat that we have already discussed, e.g have dinner. I agree that Vegans don't have eggs sounds natural, but I think that's because the omitted modifier is in their diets, so the definition of a vegan diet does not contain that item, or that item is not possessed in the definition. When it's a subjective decision not to eat something, like Muslims don't have pork, Jewish people don't have shellfish, etc and it's supposed to be referring to consumption, not possession, I would say it's a different matter. The have there sounds too much like pure possession to me, whether that may the obvious conclusion or not. It's easier to understand with pork because it's the consumible version of something, but if you said Muslims don't have apples it would most logically just be pure possession of them.