From ancap point of view you don't have right on property of others. So if you want for example post on nostr relay operated by ancap, he can blacklist you because he don 't wan't provide you his disk space. On truly free market you can't force other to providing you service when they don't want.
Also i can set my client to ignore your post, because it's my client and i can do what i want with it.
I also can tel other that you are bad person so they need to ignore you. It's their decision of they do it.

Only case when it's not free market is, when somebody want use state power to stop your spaming. So do you have exmple when ancap used state power to stop spam?