"But even if there wasn't a state, then the migrants would clash with the locals that were in the towns that the migrants were destroying"
If the state did not exist private property owners could mow them down with machine guns. There is no right to trespass onto private property. A privatized anarcho-capitalist country (or region/zone) would not have "open borders," it would have private property borders, and property owners, including groups of property owners working together, could use violence to defend their property borders against trespassers/invaders.
"If the state did not exist private property owners could mow them down with machine guns."
Just to clarify before anyone freaks out, I was engaging in a bit of hyperbole here. Property owners in an anarcho-capitalist society should of course try to ward them off with fences or walls or tear gas or some other non-lethal means first, but of course if that does not work and the situation escalates, deadly force to defend property rights could become necessary.