I'm all for privacy and the government not overstepping their bounds, but could someone please let me know why this is so bad? I'm genuinely curious.

Your social media info is Public. If you have information public, that is your own fault and the govt can access that regardless if you give them your handles or not. If they were asking for passwords and access to accounts - of course that would be a different ball game.

But simply asking for your handles (while you can easily say you don't have accounts) doesn't seem like too much of an intrusion to me.