Blockchains storing social data is good example. It's infringing by nature GDPR. A decentralised facebook-like social network on the blockchain is not possible anymore. Each node can be sue. It had happened with TOR exit nodes.
But I still don't see the connection with the first amendment.
Edit: come to think of it I'm not even sure it protects them, but again, it certainly doesn't require them to store or transmit anything.