[spondylosaurus]

I disagree. Particularly in the "vegan versus vegetarian" debate, it's widely understood that what separates the former from the latter is milk and eggs.

And in this context specifically, it should be evident that regular mayonnaise isn't vegan, since vegans don't eat animal products. Which includes eggs!

[reducesuffering]

That doesn't mean that dairy is the singular word to refer to the difference between vegans and vegetarians. Dairy is widely understood to mean solely milk products. Vegetarian is vegan + dairy + eggs. Use a different word for dairy + eggs.