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Going fur-free is more of a vegan thing, isn't it?
Vegetarians don't eat animals.
Vegans don't eat or use anything with animals or their by-products, or anything tested on animals.
So if you really want to go cruelty-free, the best way is to avoid ALL animal products. Besides, the dairy and egg industries are even crueler than the meat industry. All animals on those farms are killed too, but they are enslaved until their products are no longer profitable (ie their egg-laying and milk production declines). Their babies are taken away. The male chicks are ground up alive or suffocated. Male calves are turned into veal. And female calves are turned into milk machines, repeatedly impregnated and have their babies taken away until the day they are sent to slaughter.
So I say, go vegan, and avoid all this misery. :)