Build a wall. :)
We don’t need a wall.
We live about 40 miles from Cody, Wyoming and the cats we get are usually dumped along the North Fork highway by idiots traveling to Yellowstone. They think the cat is going to have such a wonderful life “in the country”.
The reality is that the cats usually die a miserable death when a coyote, wolf, fox, bobcat, eagle, hawk, badger, lynx, or mountain lion catches them.
If they make it to our ranch and they don’t fight with our barn cats, don’t fight with our dogs, and don’t attack/scratch our kids then we might take them in and have them spayed or neutered and then let them stay in one of the barns. If they’re smart they stay close to the barns and don’t wander because lots of things out here like to eat cats.
But our animals and kids come FIRST and any cat that comes on the property and isn’t interested in being a good citizen gets shot just like any other pest that comes here with ill intent.