Facebook friend John Newbury added this: "many are left over from the fur industry and recycled from old fur coats. Many are from hunters. here is company that does both: http://www.hideandfur.com"
Of course, it makes a difference what a vegetarian's reason is for being vegetarian, but I think he's gonna keep tying as long as the animals aren't being killed specifically for tying flies.
UPDATE 6-5-11: This, from a Yahoo.com article about the feather hair extension craze:
"...They come from roosters that are genetically bred and raised for their plumage. In most cases, the birds do not survive the plucking.
At Whiting Farms, Inc., in western Colorado, one of the world's largest producers of fly tying feathers, the roosters live about a year while their saddle feathers — the ones on the bird's backside and the most popular for hair extensions — grow as long as possible. Then the animal is euthanized."
So some animals do die for fly tying material. No more buggers or dry flies for my vegetarian friends.