This is commonly called "open immigration." Most Objectivists associated with the Ayn Rand Institute appear to be for it.
Harry Binswanger is even more radical.
This is a defense of a policy of absolutely open immigration, without border patrols, border police, border checks, or passports. After a phase-in period, entry into the U.S. would be unrestricted, unregulated, and unscreened, exactly as is entry into Connecticut from New York.
If 100,000 men from the Taliban region of Pakistan want to come to the United States, Binswanger thinks they should be allowed in, no questions asked.
Leonard Peikoff, Ayn Rand's legal and some say "intellectual" heir, is against open immigration.
Now, on the website of the eccentric Ed Cline, one Ed Mazlish has posted an outstanding rebuttal of open immigration.
A couple of the many excellent comments:
A free society with a government limited to protecting individual rights is a monumental achievement in the history of mankind - it is not the product of random happenstance or chance, as tens of thousands of years of tyrannies demonstrate. It is not something that occurs in nature, waiting for man to come and pick it off trees as though it were low hanging fruit. A free society has certain cultural requirements and prerequisites, without which it could never be created and without which it cannot be maintained. Proper immigration policy must reflect these facts and must serve to preserve the cultural factors on which a free society is based.
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The true justification for immigration restrictions is the need to protect those who respect individual freedom from those who are cultural collectivists - not the need to protect the welfare state from overload or even the need to protect innocent Americans from jihad. Even if the welfare state were repealed today and all jihadists were terminated tomorrow, the ideological requirement to protect a free, democratic, and rights respecting society from masses of incompatible cultural collectivists would still remain.
Hopefully, writers such as Biddle and Binswanger will respond to Mazlish's critique. I'm not holding my breath.