This is just a workaround. Not the correct answer. The correct fix is to use Y-Axis as Up-Axis for the FBX-Export Dialog instead of the Z-Axis.
This is what is mentioned in the unreal issue tracker (as by design) but it is a bug as Z-Up seems to work with ascii-export. It is still open to either fix this bug! or check if the FBX-SDK is failing and writing the wrong settings into the file.