Open borders are the dumbest mistake leftietarians made, and there's nothing intrinsically libertarian about the idea. Foreigners have a right to leave their countries, but they don't have a right to invade countries where they are not welcome.
Open-borders advocates want to welcome a foreign invasion which would create a far worse statist government than what we already have in white countries. And no, the abolition of the welfare state would not, by itself, put an end to mass immigration. A minarchist country would be a magnet for unskilled immigrants fleeing from third-world shitholes,but who don't understand why those countries are shitholes in the first place. Soon after, the welfare state would come back, not to speak of massive criminality, all kinds of widespread disgusting behaviour and eventually a foreign tyranny, either by democratic means or by coup d'etat.
In an ancap country everything would be private property, so the wetbacks would be trespassing. Yes, citizens would have a right to invite foreign workers into their property, but only insofar as they don't become a physical threat to other citizens.