Immigration, in an autonomous society, wouldn't simply be a matter of 'open borders' vs 'closed borders.' The situation we have now is a knotty, complicated mess of warring motivations which have nothing to do with a geographic grid or cultural integration. The state is a monopoly which deems itself responsible for guaranteeing accountability between the contract of independent parties; in other words, the state is a meta-contract. One of these contracts is private property. However, it's jurisdiction only reaches so far, which is why we have borders; the borders of various properties are enclosed within one large one. Nationalism is a solidarity myth which is further abstracted by the fragmentation of sovereignty which comes with democracy. It could never trully open its borders to everyone; it would create a double standard with its neighbors by doing so. There is nothing 'open' about not being able to pursue a thief just because he went one direction rather than another.
The state claims to keep contracts accountable to one another when in fact, it assumes its own right to breach and interfere with property within its own borders, as it constantly redefines criminal behavior to the point that one's property is not one's own.
The immigration issue is a constantly redoubling contradiction. No property owner within our nation state has a right to bring immigrants onto his property. The state would call people it didn't want 'aliens.' On the other hand, if the state decides to bring in thousands of criminals and soldiers from countries we've had violent conflicts with, it calls them 'refugees.' It is entirely an issue of agency. Once again, through representation and a bit of smoke and mirrors, the government tells people what it wants and how to feel about it.
There are no such things as borders in nation states; just territorial monopolies which trade human bodies with other territorial monopolies as it sees fit, regardless of whether or not it interferes with or infringes on the sovereignty of property owners within the (metaphorical) walls of the nation state.
The idea of 'open borders' is deception. Who is 'opening' them? What does it mean? It depends entirely on who is saying it. People who favor stronger government regulation tend to favor higher taxes, as do people who have sentimental economic plans like world peace or stopping everyone from not recycling. Often, it gets slipped into the fine print that people without visas will get free housing or schooling or onto welfare programs. Taxes, originally a forced monopoly to ensure the smooth function of interface between citizens in a given area, then turns into a means of incentivizing and mobilising people of interest for the state's use, whether that is helping people, destabilizing a country or roping together enough people to abstract the tax system in order to allocate recources for unnamed purposes. In the end, it doesn't much matter what the state's reason is. The point is that it's always coercive.
In an autonomous society, property owners would freely asscociate with whoever they wanted to bring in or not. They could hire whoever they wanted or not. In an autonomous society, property would be the largest unit which could standardize expectations. Naturally, integration into this society would be natural within the bounds of free association. All what ifs, like 'what if people abuse their power' are being performed right now by the state. Abuse will always happen, but in an autonomous society, there's no one to standardize abuse across an entire nation.