Not really. You can host your own data but you still rely on Bluesky’s services to access it. And there is no realistic way to migrate your content or audience to another platform outside their control
So ATProto that bluesky is built on has 3 core aspects. PDS’s (personal data server, stores your account content and data), Relays (transmits your actions such as likes, favorites, replies etc), and Appviews (basically the front end that you use to convert the data to a human readable front end like the bluesky app)
PDS’s are allowed to be hosted by others right now but Relays are not. So even if you host your own PDS on the bluesky network, you rely on the bluesky controlled relay to be able to interact with the network.
In theory there is a future where other people can host relays on the network but it’s not that way right now and is likely going to be too cost prohibiting for the people hosting to ever be realistic.
