Rhino documentation file: https://docs.mcneel.com/rhino/6/help/en-us/commands/block.htm says: Properties by parent
This option is only useful when creating blocks. Before you make a block, assign objects color to By parent, then make the block and include the object. The layer that is current when the block is inserted will control the color and visibility of the objects that were set to By parent.
This feature exists in wireframe and ghosted modes only. It does not exist in rendered mode. Its behavior in shaded mode is very strange - when I select one block, all blocks display the same color. Some modes display perfectly black blocks.