You know the biggest gaffe on this entire site is that everyone seems to think free range means "turn my animals loose to go wherever they want". This is not the case. Be it with dogs, chickens, ducks, rabbits, or zebras. If you want your animals to be free rangers then fine I have no problem with it. But free range these days and by law does not mean you turn them loose and let them go wherever they want.
Traditional American usage equates "free-range" with "unfenced," and with the implication that there was no herdsman keeping them together or managing them in any way. Legally, a free-range jurisdiction allowed livestock (perhaps only of a few named species) to run free, and the owner was not liable for any damage they caused. In such jurisdictions, people who wished to avoid damage by livestock had to fence them out; in others, the owners had to fence them in.
Now really do you want your neighbor's sheep, cows, pigs, horses, or zebras running over your property, eating your garden, digging up your yard, eating flowers and pooping all over your property? Pretty sure everyone here is going to say hell no. Even you yourself said you didn't want their dog on your property so how is it that you get all mad when they don't want your dogs on their property. Pot meet kettle.
These days Free Range, Free Roaming, or Pasture Raised would be defined as "livestock that have had continuous and unconfined access to pasture throughout their life cycle". This doesn't mean you let them roam wherever they want it means you give them a safe and secure area with fences surrounding the pasture to which they have access. It applies to all livestock. And when it comes to dogs and cats the laws are generally more constricting meaning that if your dog or cat leaves your property it's fair game to anyone who comes across your animal. And really they can be shot for no reason other than being in the wrong place at the wrong time and all the person has to say is that your dog was attacking someone or something on their property.
Seriously keep your animals on your property I don't care how big or small they are, make sure they are in a safe and secure area and are being fed and cared for properly.