Not necessarily American problem!
I follow my local daily news, and I always check the general public comments below the online news when related to hunting.
95% comments by non-hunters are very negative. Sometimes it goes to extremes - but in any case the hunters are always guilty by default.
For example, if there is shooting accident with two hunters involved, one ends up wounded or worse - the comments are supportive in the way that they should shoot each other more often. And no sympathy shown for the families, either.
Or, when wild boars start making damages to the crops, and in the suburbs, the hunters are again guilty, although in some cases they are not allowed to shoot near urban areas. This time they are guilty for not-shooting.
Or, when a hunter kills a stray dog in legal hunting grounds, and it gets to the news for some reason, then sh@$%t-storm goes again, with negative public comments.
I am no longer surprised by negative comments from public in urban areas.
However, rural areas are more supportive with better understanding.
Analyzing this, I beleive that it comes for understanding the nature and ecosystems, and people in rural areas, having their own farms understand this much better, then city folks. This is my view on educational stand point on general public.
However, there is a sociological point as well:
If the country, or some local area has a tradition of warriors, hunters, or martial arts - the pressure on hunters will be far less, then in other social environments.