
Okay, here's my argument for you ->
Vegetarians make a conscious choice to the abstaining from eating meat. While they will consume milk, honey and eggs, these are animal products that can be harvested without harming or killing the animal in question. Since we never see the Cullens or any other "vampire" in Twilight eating, we can only assume that those that claim to be vegetarians are in fact hunting wild broccoli, carrots and other vegetables.
However according to vampire folklore, it is not possible for these sort of mythical creatures to sustain themselves on such a diet. They need to regularly consume human blood and often kill they prey in the process. It is therefore a safe conclusion that the creatures in Twilight are in fact not vampires.
So what are they?
My initial conclusion was zombies wearing large amounts of body glitter. However zombies are know for the consumption of human flesh and are often stereotyped as enjoying brains specifically. In think it is a safe conclusion that like vampires, zombies are unable to engage in a vegetarian diet that the Cullen's possess.
If we look away from the realm of the undead, the most logical conclusion is that they are fairies. Often referred to as the "good folk," fairies are troublesome creatures by their nature. They would not see anything wrong with going into an area under the pretense of being vampires just to stir up trouble with the local werewolves.
Fairies can be vegetarian, sustaining themselves on nuts and wild berries, and more importantly would have the glittery skin which sparkles in sunlight.
If that wasn't proof enough, consider that the Cullen's are all venomous which is just flat out not possible with vampires. If they really were that poisonous, they always kill without fail every human they bite to the extent that nobody would rise up to become a vampire from it. However if we consider that these creatures are not vampires but fairies, we then realize that what they claim to be venom is really nothing more than fairy magic.
Once we take into account that magic is involved here, it makes a ton of sense as to why they are able to use it to turn humans into their kind [magic] or engage in relations that result in a human-fairy hybrid child [magic.] A half-vampire is ridiculous, but when you consider that half-elves are one of the staples of fantasy literature -- it only makes sense that other fairy races would be able to produce hybrid offspring.