I need to look into this some. I don’t think it’s FBX export itself that’s the problem. If you make a plane and make a block out of it. Mirror the block. Mesh the results. Run SelMesh then Dir. You’ll see the normals are flipped there too.
FBX doesn’t export blocks or components or whatever they might call them. It exports the transformed mesh as an individual object. So what you see in the test above is essentially what FBX is using as geometry to export.
I think this is a long standing bug with symmetry and it used to occur with mirroring as well. I have a custom view mode which shows backfaces and before I export I make sure all normals are pointing correctly. Try using the flip command on those symmetry objects and then see if the export works if not then there is something broken in the exporter.
RM