The first step to getting past this problem is to spread ... as much as democratic principles have been since the enlightenment.
I have to take a quick lol break. Democratic principles do not spread from the Western Governments, they install puppets in regions where they want resources, claim they were fighting oppressive or evil regimes, and proceed to absolutely fuck up the region. See Congo and Iran for prime examples of this. Cuba for where "democracy" failed.
Now, spreading democratic principles is in theory great. Some societies may end up working better in a democratic republic (like the US that is in absolute turmoil after a democratic election...), or a republic (rome/greece back in the day), or a monarchy (UK won the game of Risk). The West has fought several wars, overt and covert, in the name of Democracy, but mostly were for power and resources.
After so many fails at people being decent people...how could a good word of democratic principles spread?
What I mean is that most of the time when there's a civil war in some country, especially in pre-ww1 Europe, at least one of the sides wants to establish a democracy. This is because ever since it happened in America and France, the world has seen that a democratic government can be pulled off, and that made monarchy seem unnecessary, outdated, and tyrannical.
We want to do the same thing with Ancap principles. If somewhere, we can establish a society that functions just fine without a government, then people will see that government is unnecessary, outdated, and tyrannical. It's basically a faster, more effective way of convincing people it can work - because there's a real life example they can point to.
ok, sure. I buy parts of that, not really the Civil War part if you really give a good look at the south vs north US and their differences (KEEP THE GOVERNMENT OUT, vs "we own you"), at least that's how my south buddies tell me...which is totally different than northerner kids like me learn. There was a democracy, and several states, who had rights to leave the union left, then they got invaded by a more industrialized region. (again, southerners description, I like hearing their side). So where's the "I want to establish democracy" in this "war of northern aggression" thing here, where they really illegally invaded several states who had the legal right to leave the union? Democracy?"
Ehh, that was rambling, but cigarette store is closing in 5 min, so I have to come back to this. Food for thought, the south US wanted democracy because they used state rights to leave the US union and the yanks literally invaded them.
Cool with this? back in 5-10.
That's one of the biggest problems that would have to be faced when putting an Ancap society into practice, and I don't have an answer for how it would be prevented in our world today, which is exactly why there are no Ancap enclaves. They would have to face not only getting invaded from every direction, but harsh sanctions from every country that doesn't want their authority challenged.
The first step to getting past this problem is to spread Ancap principles as much as democratic principles have been since the enlightenment. There are two ways of going about this: the first one is convincing people through discussion (and memes), and the second one is to establish a defacto-ancap society, and avoid the invasion/sanctions problem I mentioned earlier. The best we've come up with is literally colonizing the ocean, which we call seasteading, but technologically, that's far from being possible. When/if it is though, the hope is that international treaties will prevent existing nations from attempting to invade or tax the seasteaders, and a crackdown won't happen until the world really starts to notice that there are people living just fine without a government, just like how the American Revolution proved to the people of France/Europe that Democracy is just as workable as monarchy.