It leaves room for non-cooperation. Although we really must define what non-cooperation means in this context.

Ending Slavery didn't leave room for the decision to non-cooperate with it, by continuing to own Slaves, or to be a Slave. Certainly depends on the specifics.

Just like Slavery was dismantled with no choice for those who wished it to continue.

Can it tolerate someone having private property?

This is a very difficult question to answer. Because it's a gradient.

Certainly it could tolerate it within a transition. You could imagine Worker controlled corporations entirely, however with private property still existing.

I also think it depends heavily on the definition of private property, which is a specific set of rules in every locality. Certainly some of those rules would be different.

But I think what you're getting at is, "What's the ideal?", and the answer I think would not tolerate private property.

But honestly, I'm not sure I believe that. Again, I can think of definitions I think work.

And if some communities wish to be anarcho-capitalist, would they be permitted, or would other communities try to interfere?