I don't know when, but at some point they stopped actually issuing any sort of card. Maybe when they quit drafting? Not sure. But I registered and never had one.
Then there's my wife who got denied financial aid for refusing to register for the selective service. She went to the fin aid office at the college and asked what the heck was going on. They explained. She looked at the guy, looked down at her chest (a 34C), looked back at the guy and just stared until he suddenly exclaimed, 'Oh!! So sorry!' and fixed it.