Exporting Segmentation to OBJ and 3D Viewer

I would recommend to use SlicerOpenAnatomy for web viewer export. See detailed instructions here.

If you export in glTF format (supported by 3dviewer.net that you show in your screenshot above) then not just transparency is correct but all segment names and even the hierarchy. See some more information and example in this post:

Example segmentation exported from Slicer: https://3dviewer.net/#model=https://raw.githubusercontent.com/lassoan/Test/master/SPL-Abdominal-Atlas.gltf