If your definition of 'vegetarian' allows the eating of milk products and eggs
Why wouldn't it? That's strictly correct. It's not his definition, her definition, my definition or your definition: it's
the definition. It's what the word
means.
Now: there's a discussion to be had about whether vegetarianism is enough and whether people should really go vegan if they are serious about animal suffering, environmental impact, etc. That's a big old chinwag worthy of its own thread, and another discussion for another day. But vegetarianism
per se does allow for the consumption of milk and eggs - it's veganism (different thing: hence different term) that doesn't.
Milk requires the birth of calves, almost half of which will be male - what are you going to do with all of those?
For myself, I wouldn't breed them at all in the first place. Supply exists only to meet demand, as I'm sure you know.
Mushrooms are of course not plants - how do you know they don't suffer (being closer to the animal branch of evolution). how do you know plants don't suffer?
Negative proof fallacy aside for the nonce (and I don't often say that), they don't have the neural equipment that we already know is associated with the subjective feeling of pain. Could we be wrong about this? Yes. Is there any evidence for being wrong about this? None whatever. Is it probable? No. Is "Butbutbutbut what about the plants feeling pain?" a dickheadish non-question typically posed by people more interested in point-scoring than anything substantive such as non-human pain, environmental degradation and so forth? Hell yes.