especially the CSAM images and videos

Each ATprotocol relay would be subject to the laws of whatever country of the entity that deployed it. So if AWS deployed an ATprotocol relay then CSAM would be filtered out by the AWS team at the relay level.

Key here is that if Bluesky the LLC spins out the directory then Bluesky the LLC would have no control over what others who have deployed the relay choose to do. So, like nostr users, ATprotocol users having issues with one relay could switch to another relay with their identity and all their data intact (assuming they take control of their PDS hosting). Each of those other relay operators would have to respect the law, but beyond that it would be up to each operator what to filter and what not.

However unlike nostr deploying an ATprotocol relay is a massive lift, since each relay is like the whole entire thing, many terabytes, and all those networking costs. You could imagine countries like Thailand or Argentina with one relay each, and some countries with multiple relays. In the US maybe one at Bluesky LLC, one at each of the clould providers, maybe one at a non-profit, one run via a foundation owned by a wealthy individual driven by personal convictions, and so on. So nothing like the massive number of nostr relays, but the general idea isn't all that different. (Again the *idea* -- if they don't spin out the directory, don't convince others to deploy the relay, don't have much luck growing the client ecosystem, all that, then that idea pretty much collapses.)

Anyway coming back to question, the ban stories making the rounds are bans by Bluesky the AppView, not the relay. Yes, the relay itself (currently the only one deployed) can be set up to filter/ban, and maybe it is already for CSAM, etc. But that's not relevant to the ban stories making the rounds, that's all AppView stuff.