I'm highly HIGHLY doubtful that it's real. Real animal fur (besides the ethical implications) is usually quite expensive. For movies, and any other business, they go with the cheapest material thing that does the job to their specifications. I don't work in movies, but I've done a lot of work in the theatre, so I have a bit of background in it.
Also when fur is on clothing, it tends to be in small amounts. Those huge fur-covered coats are all smaller pieces stitched together and even though it's most definitely fur, it certainly doesn't resemble an animal. When they're trying to replicate the caricature of a real animal, they probably wouldn't use that animals actual fur. Just thinking... cats are little, Mike Myers is big. It just wouldn't work to get a bunch of cat skins, throw them together and make a cat costume, and there aren't any real big cats with those particular markings. There are technologies that allow synthetics to be made to look very realistic.
Although I'm not 100% sure, I can't fathom why anyone would use real fur for that costume. It just doesn't make any sense. So if you want to see the movie, I'm sure you can go with your ethics intact.