You are talking about 2 different groups. The person that is driven off the ledge even though they don't actually know you are out there is an anti-hunter. That's not the non-hunter you may overlap with on the trail, or wherever. The average non-hunter doesn't care about hunting because they don't think about hunting. Its just something other people do. Maybe they have/had a friend, neighbor or family member hunts so they think its fine. That person hunted and they were a good person. The non-hunter is perfectly content buying there meat and not ever thinking about how the animal had to die. Meat just comes from the store. They don't want to see it but they don't really care if others do it because again, they just dont really think about killing animals, what hunting actually is. Now while they are out doing their thing they run into a hunter that is just done. This guy has a dead animal on open display and is tired of being nice. Well now this non-hunter has to face what hunting is and maybe they don't like it, at least not the way this person is presenting it anyway. Untimely that's their problem, I get it. However, eventually they see something encouraging them to vote against hunting. Now they have a vision of a poorly displayed dead animal from some hunter that is tired of being nice. How do they vote? Maybe they decide they are done being nice too. Congratulations, you just converted a non-hunter to an anti-hunter.
Like Corb said, we need to be loud in the right places and that is not on the trail or the roads with dead animals in tow.