But you both have no concept of communally-held property, which would afford a group property rights. No "ethnic homeland" or "regional territory".
Just one guy and his apartment or country house, or whatnot.
Discussion
You mean public land?
From what I understand, and correct me if I'm wrong, you're arguing that we need a government to protect a region of land and secure the borders, because individuals cannot do it as efficiently. So anyone arguing for anarchy, is going to get that piece of land invaded or overrun by immigrants. Is that correct?
Also some questions to understand the context:
-You mention "just one guy", are we talking about 1 anarchist living amongst statists or a hypothecal area of land inhabited by anarcho-capitalists? I wouldn't demolish a nation at the snap of a finger right now if I could, people don't understand economics and property rights, so it would all devolve into chaos and you'd most likely get another state to replace the previous one. I'm more for slowly defanging the state initially (minarchism or libertarianism), parallel economies, separating money and state, monarchies replacing democracies would be interesting, etc. Then and only then do I think that anarchism over an area of land makes sense.
-What are group property rights? Who decides what happens or is done with the property in the group? Can you take your property within this group property along with you if want to opt out?
Yes, that is correct. At least, at the present time in the West.
Area of land inhabited by anarchists
At the moment, the disposal and management of common property is decided by representatives elected by majority vote. You can take some of the property with you, but not the immobile bits. You can't take a supporting column of a bridge with you, for instance, or a school, but you can have your pension paid out while living in a foreign country.
There's a lot to unpack here, and there's no way to fully express the ideas of Murray Rothbard, Saifedean Ammous, Hoppe, etc in one post but I'll do my best. Also, your meme is describing what's going on with the current system around the world, no anarchism necessary.
I don't know your background on Austrian economics, but basically, it has been seen time and time again that government is unable to perform economic calculation over production decisions, because of the economic calculation problem. Yet...government can protect property and protect against foreign enemies, right? But, isn't protecting property just another market good? Why can government produce property protection but not apples? Defense is an economic good, it has utility and it is scarce. Individuals can produce it for themselves or acquire it from others on the market. The market for defense is highly developed, from safety locks, alarms and surveillance cameras to drones, guns, security guards and armored vehicles. Also, there are more private security personnel than state security personnel in the world.
There is no satisfactory answer to the allocation of defense resources without private property and economic calculation. Without property rights, there is no objective unit against which to measure the utility from individual allocation decisions. There is no way to allocate scarce resources to where they would produce the most value.
The reality is that defense is provided on the market already. Government defense is mostly about defending the government, not the people. They really couldn't stop the BLM riots or January 6th? Yet they managed to force thousands of businesses to close during the pandemic and lock up millions in their homes.
In a free market individuals would be able to calculate the best allocation of resources and property to meet these needs in the best way they can. Without a free market in these resources, allocation is made without calculation. Tax-funded security providers have no incentive to care about customer satisfaction or resource conservation.
Security and defense are like any other good: best provided through division of labor, capital accumulation, and entrepreneurial calculation in an extended market order. In practice, most security is provided by the market. But it would be a lot better if we didn't have a monopoly (the government). Americans pay enormous sums to police and military, but they are very unsafe. Imagine if the people of Chicago or New York had all their wealth that goes to the police and army available to them to spend on security services that were responsible to them, had no monopoly, no special legal protections under the law, no right to initiate aggression, and no ability to extract tax.
Long story short, if you can't trust the government in running things like the economy, education, transportation, etc. Why would you entrust them with something as important and necessary as defense? Also, voting harder doesn't work.
I highly recommend Saifedean Ammous' book, Principles of Economics, a great read and something I plan my children on reading too one day.