I think Fuse characters alpha/transparency channels might be broken.
To test this, I made a side by side comparison with the model next to a square tile.
The model's eyelashes (and hair) still have black edges while the tile shows a successful transparency map in the same environment:
The eyelashes and the tile have the exact same nodes and textures:
Is there a solution?
I've tried swapping out the eyelashes with copies and rearranging the noodles with no success.
The only other thing I can think of is to re-model the hair/eyelashes from scratch entirely.
[SOLVED] The problem was in Fuse when I exported to .obj : I clicked "pack textures and UVs" when I should NOT have done that.