When I export a mesh from Blender the mesh normals are completely broken inside of AccurRIG. I have exported the character with both Blender's native FBX exporter and the Better FBX exporter addon and the results are the same. If I import those exported meshes directly back into Blender they look correct, so I think this is completely an issue with how AccuRIG is reading them.
The imported AccuRIG mesh has sharps added in places they didn't exist before, which is creating the new shading issues. Removing these sharps does not fix it though. Images included to demonstrate. #1 original model, #2 AccuRIG model, #3 AccuRIG model in Blender, #4 AccuRIG model with sharps visualized (sharps I never added to the original model).
Unfortunately with this issue I cannot use the software as it ruins meshes on output with no way to fix them.