Now that PDS are available for federation, you can host all your own data. Apparently relays are now also federated as part of the PDS as well but I haven't gotten a chance to look into that aspect yet.
You can choose your own custom feed services and labellers.
The app itself (web and mobile) is open source so you can build it yourself without the default bluesky labeller or feed if you wanted to.
Even identities can be done without using any central servers by using web DIDs instead of plc DIDs.
The only thing that you have to go through a centralised system for are the indexers which to my knowledge are part of BGS. BGS is open source, it's just still in the process of being federated.
So you can use bluesky with 90% of it not under any US authority and if you give it a year that should be 100%.