This is the sort of thing I pictured when I read the title of the thread. After reading the OP, I didn’t know if I should mention it.
In old movies, hunters were often portrayed in a number of ways. There were the nasty poachers, the ones that had to poach or starve, the hillbilly subsistence hunter, the farmer supplementing the family diet, and the Nasty Trophy Hunter. Another character type I recall is The Outdoorsman. This character was an upstanding, sober, reasonable person who enjoyed The Outdoors. His flannel shirt was tucked into his woollen trousers, and he often wore an A-2 flying jacket and a fedora. Maybe he smoked a pipe. The Outdoorsman was helpful to the rangers, often helped people who were lost, and kind to the environment. He was wise and frequently was well-educated. He might even be a City Boy who only spends his vacations in the forest. The Outdoorsman was a positive stereotype of the hunter.
When I think of hunters today, the image that comes to mind is a camouflage-wearing yahoo who has at least one American flag displayed on his person or pick-up truck. He’s very conservative and drinks large quantities of beer. In short, he’s a redneck. Certainly this is an unfair portrayal; but the rednecks get the reality shows. I think that hunting may not be socially acceptable to certain people because those people and the stereotypical redneck hunter are diametrically opposed in their world-views. ‘If you’re a hunter, then you’re a hick. If you’re a hick, you’re not as enlightened as i am. If you like guns, there’s something wrong with you.’
Most people don’t fish with guns. I’ve never heard of a high-capacity assault fishing pole. The hunter stalks his unsuspecting prey with murder in his heart. He is equipped with a killing machine that he is not only ready to use, he’s practically itching to use. The hunter is a killer. The stereotypical fisherman stands next to or in a pretty river. He dresses in a manner similar to The Outdoorsman from the old movies. He is quiet and contemplative. An intellectual. He and his activities fit urban sensibilities. Many people who live in large cities fear guns. They can’t imagine themselves sneaking through a forest and coldly shooting and killing a cute woodland creature. But they can imagine themselves standing by a stream having Great and Noble Thoughts, perhaps composing some poetry or prose on the virtues of Nature. They imagine the thrill of catching a fish, and then the contentment of frying them over an open fire. They skip over the bit about killing the fish, scaling it, slicing it open, and pulling its guts out.
Admitting a broad brush for the sake of rhetoric, I think that the reason fishing is more socially acceptable in some circles is that the people in those circles see themselves as Thinkers; intelligent people who are sensitive to Nature, the cCircle of Life, The Great Mandala, the cosmic interconnections of things, and who have heard of Thoreau. They don’t see themselves as people who drink beer out of cans, drive jack-up pick-up trucks, hooting and hollering as they bounce through mud holes, and killing Bambi with an evil firearm.