This is the actual, 2004 text of the Libertarian Party Platform on immigration, which is still current, and is the same as it has always been, it is their permanent position.
COMPLETE PLATFORM TEXT
INDIVIDUAL RIGHTS AND CIVIL ORDER
The Issue: We welcome all refugees to our country and condemn the efforts of U.S. officials to create a new Berlin Wall which would keep them captive. We condemn the U.S. governments policy of barring those refugees from our country and preventing Americans from assisting their passage to help them escape tyranny or improve their economic prospects.
The Principle: We hold that human rights should not be denied or abridged on the basis of nationality. Undocumented non-citizens should not be denied the fundamental freedom to labor and to move about unmolested. Furthermore, immigration must not be restricted for reasons of race, religion, political creed, age or sexual preference. We oppose government welfare and resettlement payments to non-citizens just as we oppose government welfare payments to all other persons.
Solutions: We condemn massive roundups of Hispanic Americans and others by the federal government in its hunt for individuals not possessing required government documents. We strongly oppose all measures that punish employers who hire undocumented workers. Such measures repress free enterprise, harass workers, and systematically discourage employers from hiring Hispanics.
Transitional Action: We call for the elimination of all restrictions on immigration, the abolition of the Immigration and Naturalization Service and the Border Patrol, and a declaration of full amnesty for all people who have entered the country illegally.
I didn’t say they were right on everything, nor that I agreed with them; just that Libertarian and Libertine are really two different things.