The administrators of popular mastodon instances share "block lists" manually. That's the level of coordination.

Shared lists:

https://github.com/tootcafe/blocked-instances

https://github.com/MastodonBlocklist/blocklist

https://github.com/ticki/mastodon-blacklist

and others

No, it's instance by instance. You will see some amount of cooperation, but it's not enforced by any means just a cultural norm created by the twitter refugees to mastodon. GnuSocial has a bit of a libertarian bent, Mastodon instances have a bit of a leftist bent, and of course there's the instances which are both, so it's not really a binary but rather a spectrum. Yes Libertarian and left surprisingly to many are not mutually exclusive.

The bans don't appear to be copied from one instance to another by the software, if that's what you're asking.

What the previous poster was likely referring to is the 5-10¹ instances that are banned by most other instances with the reason "allows controversial content" or "Free speech zone"².

¹: the number banned varies from instance to instance, but it tends to be the same ones.

²: this one was used by an "anarchist" instance that appears to have more rules than most other instances.