Operating system: Windows-10-10.0.18362-SP0 64 Bits
Graphics card: GeForce GTX 1070/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 432.00
Broken: version: 2.82 (sub 7), branch: master, commit date: 2020-02-12 16:20, hash: rB77d23b0bd76f
Also broken: Blender 2.83 alpha hash f6d5a9551380
Short description of error
Setting custom normals via normal edit modifier does not affect further modifiers that use custom normals-- only the unmodified custom normal is used.
True of at least displace and data transfer modifiers-- not sure if any other modifiers use custom normals for anything.
Exact steps for others to reproduce the error
Attached file demonstrates a cube receiving radial normals from the camera, then displacing along custom normals. Apply the top most modifier (the normal edit modifier) and notice that the direction of displacement changes as custom normals are written to original custom normals.
I believe this should be treated as a bug because I think that the general intent is that applying the topmost modifier shouldn't be any different visually-- it should be what you see is what you get. (Outside of a few exceptions like corrective smooths bound to original coords, for obvious reasons.)
This behavior is also inconsistent with the behavior of custom normals set via a weighted normal modifier. When that modifier is used, it seems to affect further modifiers appropriately.
Ran into this while trying to make a live projection mesh, using techniques similar to those demonstrated in the file. Should still be doable with armatures and constraints, but that would be really fiddly.