I manage a Mastodon instance. When I disconnect from another server, I explain the reason to the users on my instance. I've never once disconnected because I disagreed with another server's politics. I have cut off servers that post literal Nazi content (like swastika flags, extreme antisemitism, etc.), content that's illegal in the USA where I live, and other reasons that go far beyond "things I disagree with". I'll continue to do so. And I get new users signing up because they appreciate that I disconnect from that filth.
And from what my other admin friends say, that seems to be the standard practice. Sure, there are some instances that disconnect much more quickly, as is their right. Most don't. The only servers that regularly get cut off from the rest of the fediverse are the ones hosting truly vile content, and by that, I don't mean "this person has people in a political party I don't like", but like their public timeline is full of people making 'kill all the black people' "jokes". Darned if I'll tell someone they're wrong for cutting the link to some of the truly, genuinely abhorrent instances out there.