From the section "Mr. Spock" in The Making of the TV Series Star Trek by Stephen E Whitfield and Gene Roddenberry:
A basic tenet of the Vulcan philosophy is nonviolence. Vulcans do not believe in killing in any form. They may hunt for the skill involved in tracking but eons ago ceased to kill the animal they are tracking. As a vegetarian, the mere idea of eating animal carcasses, cooked or not, is revolting to Spock. Even his vegetable diet is limited to the simplest of vegetable life forms.
While this does not imply a purely vegan diet, the insistence on only the simplest vegetable life suggests that eggs would not typically be consumed, but that milk and cheese might be.
Replicated food, since it was never alive, might be a loophole, but I can't think of anywhere we've seen a Vulcan taking advantage of that.