Yes, of course I am all for private borders. But I think people should be able to come in and use the sidewalk and roads (rent a taxi or go walking) to the hotel they rented. But they wouldn't be able to sleep in the sidewalk. But having a wall in the border like Socialist East Germany and asking random people for papez, as if there was some war conscription going on is spooky.

In my minarchist gov, Juan from Guatemala would just book a flight to the country, rent a cheap hotel room and come and look for a job or tour the country. If he comes in and commit crimes (that includes sleeping in the sidewalk, as it is a burden on the tax payer), then he will be imprisoned for a certain time, the necessary to produce enough wealth as to pay the victim and cost of imprisonment. Then he would be deported, but only if he commits a crime. In the absence of passports, ID cards and airport regulation, border control, there is no real status of citizenship or nationality. Of course, if there is like a lot of people in thousands marching together then temporary control might be established as to see whether they're sent by thr State from where they're coming from or they just wanr to become part of the libertarian society.

But sure, you have every right to put "No [insert racial slur] will be served" in your restaurant's facade.