libertarian is not the same as Libertarian.
The Big L Libertarian party supports open borders - look at their platform.
That's true, and it's the stupidest part of their platform. I'm really not sure how they rationalize it in the context of the Constitution, although it makes sense in the context of absolutely minimal government (which isn't what the Constitution is about; the Constitution is about limited government, not about anarchy). You could call me a Constitutional libertarian perhaps, but I am not a Big L Libertarian.