The biggest name in Libertarianism today, Ron Paul, wants to build a massive concrete-and-barbed-wire fence along the entirety of the southern Border.
The second-biggest name in Libertarianism today, Rand Paul, not only wants a fence -- he wants to militarize the Border against Illegal Immigration, with regular military patrols and everything, just like a real National Border.
I guess that you might be stuck in some hazy, unformed 1970s-era conception of Libertarianism; but the most prominent names in Libertarianism today have come to the conclusion that American Property Rights outweigh Illegal Immigrants' Freedom of Movement (Trespassing!), and have taken policy positions accordingly.
So I don't really know what you're arguing about. The only libertarians who are actually getting elected to Congress, are staunchly Pro-Border Security.
If you did a little more investigating of the world around you, you might have noticed that. (Just a suggestion, that's all).
Sorry for the double post. Mex Maxima Culpa.