There can be a libertarian case against open borders.
My friend Charles Amos - who writes The Musing Individualist - disagrees and makes the case that any immigration restrictions amount to an undue imposition of the state upon individuals’ movement. On the face of it, this makes sense - taken in isolation, it is outrageous that a group of individuals could band together, call themselves a state and proceed to forcefully restrict the travels of others. However, there is a legitimate libertarian rejoinder to this point which rests on the property rights of the people of a territory. As a late birthday present, I offer this libertarian case for some border controls in some circumstances.
Firstly, I want to dismiss a casual means-justifies-the-ends argument for immigration controls, for it won’t be a purist libertarian one. The argument would run something like our freedom depending on order, which depends on some migration controls - and therefore some level of migration controls could be justified on the basis of Under the libertarian framework in which most if not all state intervention is coercion and all coercion is wrong, then it does not necessarily follow that some coercion is justified for possible down-the-line freedoms. The libertarian wishes to limit state intervention on deontic level and/or on a negative liberty-maximising level - not on the level of preserving some holistic view of freedom reliant on order and popular support [to be maintained by migration controls].
Nonetheless, there is a strong libertarian ideal of property rights. All the same, it is unlikely that a libertarian says that the state owns the country. Rather, the country’s territory is composed of a patchwork of private properties in the libertarian view. The Lockean view of property, adopted by many libertarians, sees private property as formed by the mixing of labour with land - at which point the labourer becomes the owner of the final product. The owner is then, under a strong view of this property, free to bestow it to his or her descendants. So far so straightforward.
But this view opens the door for a) the members of the population of a country having shares in some property (as those and the heirs of those who built many public goods in the country) that they cannot reasonably exercise control of directly and b) state ownership of some property in the country. A lot of this property could be traversed almost automatically entering the country. For example, the avoidance of all roads and pavements altogether on entry to a country is pretty hard to avoid.
The construction of all the public goods of a country that are so pervasive that they are automatically used on entry to a country - such as roads or, on a more immaterial level, rule of law - is the cumulative work of the people of a country. Therefore, it is largely the members of the population of a country who (under (a)) possess shares in the ownership of these public goods. Clearly, random members of the public are not in a position to defend this property as they wish. They are in need of a steward, just as the incapacitated patient needs someone with power of attorney to manage their assets. The available steward - with at least some modicum of representative legitimacy (in a democracy) and the faculties to adequately manage and protect the property - is the state. Therefore, there is a case for the state to act as the steward of the public’s property in this case. This can include controls over who else has access to this property.
Additionally, the state could legitimately own a lot of this infrastructure. Most libertarians believe in the legitimacy of some form of legal personhood of organisations. So under this view, if an organisation mixes its resources to create a new product. The state does this with its public infrastructure. Even if the state has illegitimately obtained those resources (e.g., through unjust taxes), that does not render the activity of constructing the public infrastructure illegitimate per se - it just means that the state also owes reimbursement of what it’s taken to those from whom it took or their heirs. Given the state could legitimately own this infrastructure and is unlikely to owe any ill-gotten gains to people seeking to enter the country, it would be legitimate for the state to create and enforce policies over who makes use of this infrastructure. This is practically the same as instituting immigration controls.
Therefore, immigration controls are not necessarily unwarranted restrictions of people’s movement even under a strong libertarian view.
Note: this does have a pretty radical right of return implication (and unjustness of the state restricting this)… unsure how I feel about that. But this argument does nonetheless justify, from libertarian priors, some sorts of immigration restrictions operated by the state.
Note: one refrain offered by Charles is that arguments for the legitimacy of immigration could justify internal immigration restrictions. But this is not particularly relevant where the state is operating as a steward for the property owned in part by the vast majority of the public across the whole territory - and it is certainly not relevant when the state is treated as the owner of the public infrastructure to which access is in question (where the state decides it sensible to grant existing residents of its territory access and be more selective otherwise).