From Jacob G. Hornberger, who ran in 2000 for the Libertarian Party Presidential nomination and as an independent in 2002 for the US Senate in Virginia:
There is a common perception that there are two alternative libertarian positions on immigration: government-controlled borders and open borders.
Nothing could be further from the truth. There is only one libertarian position on immigration, and that position is open immigration or open borders.
After all, government-controlled borders and open borders are opposite positions. How could opposite positions on immigration both be consistent with libertarianism? That’s just not possible. One is consistent with libertarian principles and the other isn’t. If a position that purports to be libertarian isn’t consistent with libertarian principles, then as Ayn Rand would have said, “Check your premises.”
Why do many libertarians believe in government-controlled borders and oppose open borders?
For the same reason that there are many libertarians who believe in the national-security state, an enormous standing army, and selective foreign interventionism: they came into the libertarian movement as conservatives, owing primarily to an attraction to libertarian free-market economic principles, but unfortunately have been unable to let go of their conservative views on immigration (as well, for some, on foreign policy and other issues).