This is very relevant to libertarianism. In fact it is one of the most interesting and cutting-edge debates in the libertarian intellectual space.Perry Mason's confusion here lies relative to the nature of the current world we live in. From roads to sidewalks and public transportation, we live in a world where government is a monopolist in many areas, This monopoly situation results in no free market exchange/calculation between use and payment,
The answer to your last question is that "these people" have no right to enter anyone's property, without an invitation, in a private property society. So why do they get to enter "public spaces" and use public resources (welfare, roads, whatever)? I don't mean that as a rhetorical question, but a genuine one.
Much as been written on the fundamental question - how to treat public property and the exclusions of persons from it.
Great libertarians Hoppe and Block take opposite positions on this issue. So I cannot agree this has "nothing to do with libertarianism."
We all recognize this fact, even libertarians. There is no libertarian that I am aware of that claims that no one should use roads and sidewalks because they are public property.
It would be quite frankly absurd to take such a position.
But what if I am a plant owner and pay taxes, from real estate taxes to income taxes, on my business to support the building and maintenance of roads and sidewalks, what libertarian is bold enough to tell me how many undocumenteds I can hire, because they use roads and sidewalks, given I am paying taxes far greater than any lone individual for construction and maintenance of roads and sidewalks?
Let also imagine that I own an apartment complex where I pay real estates taxes and income taxes far exceeding the cost of my personal use for roads and sidewalks. What libertarian is bold enough to claim that I can't rent to whomever I want and grant that person permission "to use my part of taxes paid" on roads and sidewalks for my tenants?
Of course, as I have pointed out, with government in the mix it is bizarre to attempt to make exact cost/revenue-paid calculations but it is equally bizarre that a libertarian should claim that, as a landlord or business owner, that people I rent to or hire, when I have paid taxes on a property and income, should not be allowed to enter into exchanges with me.
This is not a great looming libertarian question,
The libertarian solution is a Private Property Society. The problem is that we live in a world of government and just because there is government doesn't mean individuals should be barred from hiring people because of where they were born or renting to people because of where they were born.
The solution should be less government and fewer government regulations or does a libertarian seriously want me to ask, "Papers please?"