Lab grown fur is an interesting prospect. We've got (almost) industrial scale lab-grown skin and a quick check with a friend who knows much more than I informs me that she can't think of any barriers to growing fur this way. You could even insert chemical/genetic markers such that one could guarantee that a given piece of clothing was made from lab grown and not "real" fur.

Also, not a huge fan of mink. Other furs, perhaps. But not mink.

As a second aside, if we could produce fur, what about human hair, for wigs? But you'd likely have more regulatory issues with human hair than otherwise.