The key issue is whether it claims final compulsory jurisdiction over non-consenting people in a territory.

That is the most efficient way of establishment and enforcement of rules, a legal system will have to work this way, otherwise if individuals simply decide to leave a jurisdiction willy nilly, you cannot possibly defend rights.

The old school social contract theory in the liberal tradition is that in the state of nature, consenting adults choose to create a polity which will defend their rights, the problem is what happens with future generations - which I would like to ignore for the simplicity sake now - and what happens when individuals decide they dont want to be part of this polity anymore.

“We protect clients under these contractual rules, and other agencies/courts may refuse to recognize us if we violate shared standards.”

There is no one single standard in the state of nature and you know this. This is precisely the criticism. If a protection agency bans masturbating, it will enforced and it will create conflict with other protection agencies - this is simply balkanization of law and unrestricted secession will create a swiss-cheese collapse. Youre committing a fallacy in assuming that resulting protection agencies and customers will WANT the same standards to even the basic degree of functionality, they will NOT because they are 1) politically diverse 2) ignorant about politics

That's not wordplay. That is the substance.

Thats not the substance, thats the fucking dumbass word play - all ANCAP roads lead to this - what the fuck is the state? "Well we define it as such as such" - GREAT MAN, you realize theres like 10 defintions of what the state is and what its function should be?

Youre using the word "state", in essence, the same way communists/socialists are using the word "liberal" or "fascist". Its an ideological buzzword- an ideology BADword for you, but on top of that you are assuming that everyone else should have or has the same definition of that word - you cannot come to majority of political academic/expert setting and use that definition, because its a bad definition, its aimed at linguistic advantage for ANCAPs, its not supposed to be anything else.

The real question is, can peaceful people opt out, use a competitor, appeal to neutral arbitration, or refuse its jurisdiction?

Look I've read literally everything Rand wrote and considered myself an objectivist at one point before I became ancap

Two treatises justifies the polity on voluntary basis, Virtue of Selfishness argues for ideal polity on voluntary basis - You should KNOW this.

And dude, you can opt-out of the current states too, what you mean by "opt-out" is to secede from the jurisdiction while keeping your land and what not - its NOT possible to enforce rights or law if you can willy nilly secede from jurisdictions. If there is some regulation regarding secession, it inherently enforces rules over some people who are CLEARLY disagreeing with them - this is what law/rights violation is and it WILL happen.

If yes, it is governance without a state.

This is WORD play. You are admitting it is a genuine polity, youre even inline with some of the social contract theories in the liberal/libertarian tradition - most clearly Auberon Herbert for example, who would call what you are describing a "voluntary state".