So does Bluesky app have control over what data it aggregates and can decide (without checking with a user) not to aggregate data from a host? I am trying to understand what are the implications for a user, and a bad scenario where one would disagree with an action of the app.
And if the answer is "yes" then at least when someone "makes their own app" can they easily use "Bluesky hosts list" + add special extra hosts (or remove specific hosts) so that the app relies on the platform, with the exception the disagreement point?
Yes to both.
An app can choose to ignore/ban some users (or even entire hosting servers if they’re specifically created for network abuse). This is similar to how any web app may choose to ignore POST requests from spammers.
And yes, someone can decide to aggregate data themselves and provide an alternative app over same data with different moderation policies. In fact that’s already the case (Blacksky runs their own application server that mostly piggybacks on Bluesky moderation decisions but overrides some of them. There are also clients that ignore moderation altogether and show you the raw data from hosting.)