Private borders are not in dispute, except as straw men, or by Marxists. Bordertarians fail to recognize that many Real Life private borders are “open” for good reason. Consider a shopping mall: borders to the privately-owned property are open. The privately-owned access roads and parking lots are open on purpose, because the mall wishes to attract people. The mall itself usually locks its doors at night; it is usually open to anybody except those who have been banned for cause, such as known shoplifters. The stores within close their gates after hours, but are open to all, with similar exceptions, during business hours. Within the stores, there are areas with more restrictive borders, such as employee areas, management offices, and so forth. There are still more restrictive borders where it matters, such as the door to the bank vault.
Privately-owned borders include examples of all degrees of open and closed, depending on the requirements of the owners.
Bordertarians seek to apply a single one-size-fits-all “solution” to the entire external border, and to every border within. They effectively collectivize access to all property, since they mandate who may and may not be on all property. This is destructive of private property norms, as anyone who has been raided by immigration authorities may attest.