Plenty of Libertarians are open-border proponents.
Yes. First of all there are libertarians and then there are libertarians, almost opposing definitions of one another.
But I'll start with myself. I am more a libertarian than anything else. Being such, as a young idealist, I was always pro open trade. It's best for the consumer to have the most choices, this leads to the natural settlement of prices on the intersection of the demand/supply curve to make everyone win-win.
It is also best to allow unfettered immigration. (Again, libertarian
theory.) If you think of it like air filling a vacuum, when there is a market need for employees, or for more private enterprise because of a growing population and thriving economy, and there are places in the world where there is an overpopulation and no work opportunities, humans will migrate to the locations needing more humans. This eases the pressure on the sending side and it fills the needs on the receiving side. All well and good, right? Pure libertarian philosophy, believing in minimal rule from above and maximum freedom of the individual, suggests no borders is the ideal condition that leads to maximum happiness for all.
Well like all purist ideas, this doesn't work so well in the real world. Take trade with China for an example. Because of completely different political, regulatory and monetary landscapes, instead of benefiting everyone, it has become a complete disaster for the U.S. and a pretty good thing for China, and a very unbalanced thing overall. The prices cannot settle on the demand/supply curve to make a win-win for all, because the curve is corrupted by these differences. There is not a level playing field, and this is the problem with ideals. (They often assume things not real.)
The same with immigration, it is a mix of good and bad, it is not, as a purist libertarian might argue, always a total good thing to allow individuals to move and live where ever they want. You can never have a utopia and that includes a libertarian utopia. If you believe open borders leads to the best overall result, you must assume everyone else holds your ideal of libertarian freedom. But they don't. For example, if your open borders allows a lot of fundamentalist Muslims in, they'll eventually vote in Sharia law, and where are your libertarian liberties now?
Natural law trumps all, including libertarian, or any other, political philosophy. And natural law leads humans to invade and destroy; cultural destruction by immigration counts as that. So I have come to see that this given group of humans (the U.S.) must protect and defend itself from anything that will transform us away from whatever it is that makes us the most free and prosperous nation in the world.
This does not mean I am against immigration. It means I am against illegal, uncontrolled, excessive immigration from groups who will not assimilate and adapt the values that make us what we are.