Well, as Milton Friedman is attributed to saying; "You can have a welfare state or open borders, but you cannot have both."
Many migrants coming to the U.S. and U.K. are specifically allured to the prospect of free-loading off a system that steals from its populace through taxation and those advocating for this immigration (the left) are advocates for such a theft and various other statist programs. Indeed, these immigrants serve as the voting-power and the justification (as protected minorities) for a whole host of statist programs and policies.
I oppose this immigration because it is statist immigration.
Likewise, I oppose immigration without specific invitation. Anarcho-Capitalism is opposed to a state, any state, and a third-party monopolist of coercion telling property owners who they can hire or what goods they can purchase is contrary to AnCap ethics.
Hence, the AnCap objection to tariffs and immigration, ethically, is that the state is wrongfully preventing a voluntarist invitation for workers or goods through free and non-violent exchange.
However, this also means that property owners have the right to invite no one or buy from no one. Hence, regardless of whether economic and social isolation is a good judgment for a property owner, it is their implicit right to act in such a way.
Hence, the issue of immigration for AnCaps is a matter of what individual property owners want to don't want, its up to them.
So If I am a racist and only want white christians in the town that I own on my property, I can only allow white Christian peoples in and products made by other white Christian states/lands; however, my neighbor has the right for his privately-owned town to have complete free-trade and complete open borders; however, if he invites a bunch of jihadists and they trespass on my property, I also have the right to kill them.
Simple as that.
So am I open borders? Yes.
I am open borders and free-trade in the sense that private property owners should be able to admit whoever and whatever they want onto their own land.
But I supported Trump's wall and oppose islamic immigrations because they are uninvited tools of statism.
So to those lefties who think Ancaps are inconsistent.....
Ban all welfare and make private property and gun rights absolute and then we can talk about dissolving the border (so long as we dissolve tariffs with it).
Not until then.
"It is when a people forget God that tyrants forge their chains. A vitiated state of morals... is incompatible with freedom."
- Patrick Henry