So, when you post to a community, you’re posting to the local copy of it. Your host then forwards that post to the site that houses the community. When you’re banned from a remote site, nothing interferes with this process until the local host forwards things along. By that time, you’ve already posted.

Now, the site that’s housing the community is responsible for federating content it receives back out again, so while you can continue to post to the community locally, those posts won’t make it to any other copy of the community. But because each instance’s copy of the community is quasi-independent from each other, you can, IIRC, still engage with other local users in that space.