Anthony de Jasay takes an "on the one hand, on the other hand" approach to immigration.
One strand of libertarian doctrine holds that it is precisely private property that should serve as the sole control mechanism of immigration. Immigrants should be entirely free to cross the frontier—indeed, there should be no frontier.
...A very different stand can, however, be defended on no less pure liberal grounds. For it is quite consistent with the dictates of liberty and the concept of property they imply, that the country is not a no man's land at all, but the extension of a home. Privacy and the right to exclude strangers from it is only a little less obviously an attribute of it than it is of one's house. Its infrastructure, its amenities, its public order have been built up by generations of its inhabitants. These things have value that belongs to their builders and the builders' heirs, and the latter are arguably at liberty to share or not to share them with immigrants...
The other hand uses metaphors with which I would quibble.
First, it uses the family metaphor for the state. Attributing family-like qualities to the state is inherently statist and illiberal. Better to think of the state as an impersonal arrangement among consenting adults.
Second, the other hand appears to equate trade with sharing. In order to share with the poor, I must sacrifice. But I always gain from voluntary exchange with the poor. If the native-born intend to profit when they rent space to immigrants and buy labor services from them, then these are economic transactions as opposed to sharing.
I am not saying that there are no arguments against immigration that I would accept. However, these particular arguments seem unpersuasive.