Inexperienced trappers will likely trap pets and other non-target animals.
Backlash will ensue
I think people should be prepared for many non-target animals to be taken with snares and traps including pets. It takes years and years for government employees to learn how to properly trap and snare wolves without taking non-target species and there have been incidents where pet dogs have been trapped even by experienced trappers.
Snares are another story altogether. Stories of pet dogs being snared around the neck are heart-wrenching and death ensues quickly. Oftentimes the owners don’t realize what is happening and are unable to release their dogs from these killing devices.
This being said, I think there will be an increase interest in wolf trapping by inexperienced trappers who will trap on or near heavily used trails and roads. I’m sure that you can imagine the bad press that will ensue if this does happen. This is a very misguided decision and it will possibly result in a strong backlash even from those who aren’t paying attention to the wolf debate.