Although the information can't be removed from the Steem blockchain, it could be filtered out by the Steemit website.

So the government wouldn't need to shut down Steemit. Rather, they'd just enforce some filtering.

This would be the same as how governments force Google to filter their search results. They don't shut down Google, and they don't shut down the internet, but they force Google to make some parts of the internet less accessible. Same would happen with Steem and Steemit.