I completely understand the want and need to protect your property from intruders, animal or human. But calling for the death of any and all animals that enter your property is borderline psychopathic IMO.
There are humane ways to deter animals from entering your property. Something as simple as spraying a cat with water will deter it effectively - no need to murder it. Other options include putting down plastic spikes (that don't cause injury) on garden fences, growing certain plants which cats dislike the smell of, or even sprays that cats dislike.
And for future reference; if your neighbours cats are pooping in your garden beds, keep the surface of the soil moist. Cats (generally) won't dig in wet soil, and will instead find somewhere else to go. And your plants will appreciate the extra water.