I think you could actually throw the X-Men movies in with this as a direct comparison. Things would no longer be comprehensible for most people, and humans naturally fear things they don't understand (Remember the phrase from the dad in The Croods? "New is always bad. Never NOT be afraid.") That would cause worldwide chaos if we sprouted up out of nowhere just like the mutants did in X-Men. I know you and I would probably look at a bright blue anthropomorphic wolf walking on two legs and go "no f*cking way, this is REAL?!" The majority of the planet would not. We would likely be murdered by the thousands (saying that there's 7,000,000,000 people on the planet and let's say that 10% of us are furs, that's 700 million new animals running around. That's twice the size of America. If we randomly popped up, my estimate is that 1/2-3/4 of us would all be slaughtered within 24 hours time, provided the rest of us could escape or had people who understood immediately what was going on and could help us hide or escape. If we were to be rounded up, that might mean that a small percentage of us would actually be captured and sent to labs for the men in the pretty white coats to say hello, the rest of us that put up any kind of resistance would be killed as "aggressive hostiles" (Think the Maximum Ride series on this bit). Even if "they" managed to figure out how we all changed, we would either become lab experiments or exclusive military prizes, with either a "serve or die" ultimatum.
Now, I would love to live in a world where I could be a royal blue anthropomorphic wolf that walked on two legs and wore a button up shirt, but we can't even get along with each other as humans.
TL;DR: This would end in complete disaster, and I fully believe that World War III would start within days of the worldwide transformation.