On my boat the fur on the overhead as you enter the cabin door was falling off. I removed it and tried covering the area with vinyl but due to the heat on the overhead the glue didn't hold up. I ended up removing it, cleaning up the entire area using acetone and painted it white with a marine topside paint. In the V berth I covered over the fur on the band that goes around the berth with vinyl, there's a pic in my album. Sailrite has a head liner material that stretches as you work with it making application easier.
I recently had pretty good success cleaning up the existing fur with Folex and a cheap hand held steam cleaner that we bought at Bed Bath and Beyond.
Monkey Fur acts like an air cleaner trapping every particle of dirt that's in the air. Whoever thought this would be a good material in the marine environment should be made to walk the plank!