This was tricky for me too, as the furs are hanging above. You may need to guide your crosshairs a bit to the left or right of the actual fur, to get the interaction button. For some reason, being "dead center" doesn't activate the pop-up option.

I finally got the animal skins to light up. I ran into the quest giver in the cavern where you have to defeat a spinners red monster(I don't remember the proper name sorry) not too far from the trees ramp. Then as you go up the tree all the way, you run into the quest giver again, saying the same thing. I went at this point, having not defeated the spinner's red monster, and got the hoarder blood and flesh from the first mammoth. Eeewww.... that's when I ran into problems with the quest indicators not lighting up at the animal skins. After trying everything I could think of, I went back into the cavern near the lowest ramp, killed the red monster thing, and then back up the ramp and the indicators were working. I was then able to finish the quest.