He may not care for Pit bulls and I also respect that, however advocating going onto someone elses property and shooting or poisoning a chained up dog of any breed especially when the dog has done nothing but breathe and bark is especially low life. Chain any dog up and I guarantee you he'll bark at you when you walk by.
If the dog bothers you in your own yard or in the street, then by all means, dispatch said dog immediately.
Otherwise man up and talk to the dog owner and then follow proper procedure and be a good neighbor as you expect out of him. If no satisfactory results are reached then get together with the other neighborhood property owners and start an HOA and specify No Pit Bulls in the covenants.
I does seem to escape those who advocate killing all Pitts onsite no mater where they are that those Pit Bull owners may just own a firearm too and mabe they are just a little more accurate and faster than you may be.
Just as you would, They would almost certainly be highly concerned by some numbnut walking around their yard shooting at their dogs and who knows what else.
What if the dog chit in his wife's azalea's?