So, border enforcement is OK as long as it's private property. I think the majority of the land across the border is privately owned,
Which makes building a big wall across the border a violation of the owners' property rights, of course.
And also mean that if the owner wants Mexicans to come onto or across his land, then he should be allowed to let them, regardless of what the INS think.
or would become such in a free society. It's OK to shoot he Mexicans then, right?
Nope, firstly because trespass doesn't work like that. First you have to tell them they are not welcome on your land. Then you have to have evidence that they don't intend to leave.
Beyond that, we can ask whether shooting them is proportionate to the offense.