Have you heard of drones being used to smuggle guns? No physical person even needs to cross a border now. Personally, I can't think of a practical solution to this.
Better air space monitoring. We need to develop technology to accurately detect small drones anyway since thats the direction a lot of militaries are going.
Anything that's capable of detecting drones would get hella false positives from birds/bikes/cars/people. There's a reason radar usually ignores movement under a certain altitude.
You could detect via radio signals, but fly-by-wire drones are already a thing, perfect for short distances, like what you'd need to move a package over a wall.
It probably can be done with some combination of signal sources. Yeah radar alone doesn't sound great. It might be possible combined with computer vision, other computer signal pattern recognition, etc. Whoever gets a decent system like that working would have a lot of sales for it.
Guns, drugs, pornography, refugees, factual information contradicting or embarrasing the powerful.
You might see a moral difference, but it's all the same from an enforcement perspective. It's a thing, and you want to keep it out. The real question is how much control you trust them with.