The best libertarian position on immigration is non-aggression, which is the core principle of libertarian ethics. If a person emigrates to a new place, is respectful of his new neighbors and their property, works hard, buys goods and services from willing buyers and sellers, and lives peacefully, it is hard to find any libertarian basis for violent action against that person. If a person moves in and lives a life of thievery and violence, that is no more and no less blameworthy for a person who came from another country than it is for a person from another location within the same country. The same measures that would be properly employed against a domestic criminal would also be applicable to an aggressor from someplace else.
Libertarians who reject socialist central-planning of the economy should not abandon their skepticism when it comes to planning the optimal size and composition of a local population. If the local bureaucracy cannot rigorously determine the appropriate quantity and qualities of bread production, how much more likely is it to be successful in determining the composition of the local workforce?
Libertarians should be suspicious of all government programs that attempt to restrict natural, voluntary immigration. These interventions disrupt normal market processes and hamper economic growth.
Libertarians should also be suspicious of government programs that attempt to drive mass migrations for political reasons. Many of the greatest migrations in human history were instigated through government action, including the expulsion of Jews from Spain in 1492, the Huguenot persecution in France in the 16th and 17th centuries, the Trail of Tears in the mid-19th century, the Jim Crow system in the post-war American South, and the Partition of India in 1947.
This question is from Faith Seeking Freedom: Updated & Expanded, available in paperback, PDF, and Kindle.