Agreed - unless a dog is 100% of the time with other animals and watched all the time they will not be trustworthy with other animals. This is why farm dogs are raised with the animals they work with (cattle dogs, sheep herding dogs…). Farmers here keep their farm dogs in the barns with their livestock - same as sheep herding dogs, or LPD.
Of course these days one rarely sees livestock dogs around here, most farmers have sold off their livestock and just grow crops. But I remember well dogs coming to greet me whenever I would visit farms, I also remember seeing flocks of chickens everywhere. Most farmers had a flock of chickens, the dogs never seemed to bother those chickens.
What’s changed? Is this progress? Our kids are missing out on a whole wonderful world of playing these days I feel. Used to be farms had dogs and kids and chickens all running amok 
