The starting argument employed by libertarians and/or anarchists who support government border enforcement is technically valid, that if some thief steals my stuff and buys something else with it, that thing he bought with my stuff is rightfully mine and I can retrieve it from him, even by force if necessary.
But the people who use that argument as it applies to borders do not seem to recognize that there are many people who are US citizens and yet pay no taxes - in fact, they may be net beneficiaries of tax money in the form of welfare. Yet no border-supporting libertarian ever, in my experience, has tried to claim that they're trespassing. It's only about foreigners.
Except in a case where the State actually committed theft from a Native American tribe, or used eminent domain, or something related, the State rightfully owns the property. They are maintaining it using stolen funds, but their ownership is valid. It is only their jurisdiction (kind of a forced half-ownership) over "private" property which is infringing on anyone's rights. Taxpayers have no additional right to the land than a foreigner or non-taxpayer, because no one has a right to that land. If the State dissolved, their "public property" would revert to being unowned, not collectively owned.
However, the goods and services rendered by the State are more complex. While in theory the taxpayer should have more of a right to such things than non-taxpayers, and by extension foreigners, it is not really possible to figure out exactly what share of each good or service belongs to each person. While it would certainly be nice to think of such things as being rightfully owned by the taxpayer, some wrongs are unrightable. Figuring out what share of a building belongs to each person is virtually impossible. Shares of a service doesn't even make sense, because once the service is rendered, it's an action over time, so you can't "own" a service. The money expended on services is gone forever. The money expended on goods is not necessarily gone, but determining rightful ownership is impossible.
We can, though, say that the taxpayers own at least some of each good purchased, and that non-taxpayers do not have a right to them. But this is yet another argument not ever put forward by the so-called "Bordertarians".
The only point of a government good or service is to be available to everyone, even non-taxpayers. If that were not the case government would be pointless and likely would not even exist, thus making this entire debate moot. Given that government does not consider non-taxpayers to be trespassing when inside a building, or using a road, considering a non-taxpaying foreigner to be trespassing is logically incoherent. Either none or both.
The reason I support open borders is not necessarily because I am following the logical progression of the rightful owners of government property. It is because in the absence of government there wouldn't even be borders, much less "public property", so open borders is the nearest approximation of that at the present time.
-SB