Blockstack uses a storage system called Gaia, which in a nutshell acts as an overlay on top of existing commodity storage systems (including cloud storage, your personal server, decentralized storage systems, etc.). Blockstack apps like Graphite Publishing interact with the user's data via the user's preferred Gaia hub. The Gaia hub holds the user's storage credentials (if applicable) and uses a storage driver to store data to the underlying storage system, so applications don't have to care about interfacing with a specific storage implementation (Gaia and Blockstack implement their own authentication mechanism for applications). In the default on-boarding flow, you get signed up to use a Gaia hub that uses Azure blob storage to host and serve data.
That said, if the operator of your Gaia hub's underlying storage system can determine that content you store is objectionable, then it would be obliged to take it down. However, to prevent such power from being abused, the user has the ability to switch Gaia hubs and migrate their data between Gaia hubs. If you notice someone storing objectionable material in Blockstack, you should notify the user's Gaia hub's storage provider so they can take the appropriate action.