We must not forget libertarianism is not a teleological dogma striving for a certain end; it rather sees individual freedom and rights as the natural point of departure for a just society. When people are truly free, whatever will be will be. Hence, the question is not what the effects of a certain immigration policy would be, but whether there should be one at all.

From a libertarian point of view, it is not relevant to discuss whether to support immigration policy A, B, or C. The answer is not open borders but no borders; the libertarian case is not whether private property rights restrict immigration or not, but that a free society is based on private property. Both of these views are equally libertarian — but they apply the libertarian idea from different points of view. The open borders argument provides the libertarian stand on immigration from a macro view, and therefore stresses the libertarian values of tolerance and openness.[2] The private property argument assumes the micro view and therefore stresses the individual and natural rights. ~Per Bylund, Mises Economics Blog

Even if we grant that this is a fairly extreme libertarian view of the question, what is there to do but laugh this to scorn?