Short description of error
Until Blender 3.0, I used to export all geometry as .obj, and the result had all correct normals as in the .blend scene, even mirrored collection instances; but in 3.1, mirrored collection instances are exported with flipped normals.

Exact steps for others to reproduce the error
to reproduce the error, create any object and place it in a collection, add a collection instance of that collection, mirror it on any axis, export in .obj.
You will have to flip the normals of the objects of the mirrored collection, and you have to clear custom normals to avoid the "dark color display"

Honestly, this behaviour could be logically correct, because the geometry is flipped on an axis, but I don't see any use case in which you would want your mirrored collection with the opposite normals of the original obect.

BTW, thanks for the new exporter, it's super fast

System Information
Operating system: Windows-10-10.0.19043-SP0 64 Bits
Graphics card: Quadro RTX 5000/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 472.98

Blender Version
Broken: version: 3.1.0, branch: master, commit date: 2022-03-08 18:16, hash: rBc77597cd0e15
Worked: (newest version of Blender that worked as expected)

Short description of error
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Exact steps for others to reproduce the error
[Please describe the exact steps needed to reproduce the issue]
[Based on the default startup or an attached .blend file (as simple as possible)]