[evilduck]

In addition, dinosaur feathers that have been discovered have been in fossils where it's obviously still part of the animal, or preserved in amber where feathers were unexpected and it raised questions.

Who's been looking for neanderthal fur at any scale? It could be hiding in plain sight. AFAIK, geologists and archeologists don't try to run DNA tests on every bit of biological matter they come across. Humans are known tool users and clothing (and fur) wearers. If someone found fur near a hominid and it wasn't on their head, would anyone be jumping to this conclusion?