This may be deeply controversial, but think about it:
real fur is a renewable resource. You can easily breed animals. Lots of non-natural fibres come from non-renewable resources like oil/coal. If you live in a very cold country, it is "greener" to wear animal products for clothes and boots than to use artificial fibres. It is also warmer, so less natural material needs to be used than artificial. You may say that we should restrict our meat-eating to sheep-meat, ( which disagrees with some people) and restrict our animal-resourced clothes to wool, but many people can't wear wool, either. Also, production methods for artificial fibres is far worse for the environment than production of animal-based materials.