Am I overreacting? I don't think so. Subtle messages like this are the product of people who either have no idea they are being offensive, (which I doubt) or intentional, (which I suspect). The advertiser is making a joke, and it is not very funny. The term "pansy" is so blatantly homophobic that the "joke" won't work without it.
If you find this not so funny, why not write the group that underwrites the billboard, the National Sport Shooting Foundation.
I received this letter from the National Sport Shooting Foundation regarding the billboard;
This was not placed or approved by us. It was taken down 2 hours after we were made aware of it
Mark E. Thomas APRManaging Director,
Marketing Communications National Shooting Sports Foundation, Inc.11 Mile Hill RoadNewtown, CT 06470-2359