So, apparently, this has been a problem in cycles for years, where a transparent object has a black line where it intersects with another object. Doesn’t look like they’ll be fixing it very soon. Someone on the first thread suggested trying to mask part of the mesh with vertex groups, but I tried, and if you mask even one vertex of the feather mesh, the whole thing disappears. So, I’m not sure what do do. If anyone has any suggestions, I’d love to hear them!
https://bit.ly/2O36GjT
https://developer.blender.org/T85840