The dog is tough and vicious for protection, not only against hoomins. Now how is that dog going to keep bears, wolves, coyotes, and cougars up off of your livestock if he's on a line or penned up?
[...]any more than they have a right to point weapons at a visitor for visiting to ask a proper question.
Heh. I take it you haven't been up the Kootenai. It is not even considered to be impolite to be met with a gun, till folks know what you are about... And it is YOU that disarms, not them.
People have every right to shoot dangerous dogs on the loose.
That's a fact. But shoot the dog for doing his job, and you will likely have to deal with the man too. Or you can go complain to the sheriff or the fish and game, but they'll just laugh at you and advise you to stay in town.