But they are acting as bullies, both in the hypothetical example, and in several real-life cases. If a hypothetical right involves causing harm to others, maybe it's not the right one first suggested.
Them being "bullies", whatever is meant by "bullying" in this context, doesn't deprive them of their right to own their instances or align with administrators with similar moderation policies. Fediverse is literally built on the idea that people own their instances and therefore all own the choices they make that affect these instances, just as you own the choice to call their flocking behavior "bullying".
Or, in other words, what are you expecting? It's their hardware and their software. If one pays for hosting, and owns the software, then - unlike you or me - they're entitled to do as they wish with their stuff and to bear the consequences of any moral judgments they make. Which is the same as Twitter, same as Threads, same as Bluesky, just on a smaller and more interconnected scale.
A lot of people would say I'm transgressing my bounds if I try to use the influence I gained by paying for my server to threaten you into changing what content your server serves to your users. That's the essence of "block X or I'll block you."
And? They have a right to do so. In particular, they have a right to defederate any server for any reasons - which includes mine, yours, or this other person's, with or without asking things like "block X or I'll block you".
Or, in other words, what are you expecting? It's their hardware and their software. If one pays for hosting, and owns the software, then - unlike you or me - they're entitled to do as they wish with their stuff and to bear the consequences of any moral judgments they make. Which is the same as Twitter, same as Threads, same as Bluesky, just on a smaller and more interconnected scale.