Some 'campsites' are more crowded than a barber shop on Saturday afternoon in that your naighbor may be within conversation distance. Nat'l Parks regulate such things as fires, noise, pets, and things that go 'boom'.
In the remote areas, folks just out for a hike would'nt want to be confused with Bambi, so the discharge of firearms aren't a good idea there either.
The Nat'l Forrests have controlled hunts...ask about a hunting permit. There are State Parks, Nat'l Parks, Nat'l Forrests, and, I think, BLM (Bureau of Land Mgt) Parks. You have to know where you want to go and chose your own comfort level. Some places you can rent a bungalow.
Legal, most likely not. But we were fairly well armed anyway. The bride and I used to take the kids camping around the Big Bend area here in Texas. There was always some sort of sidearm close to hand, usually a Mdl 24 or a 629. A Ruger 44 Carbine, and a take-down Marlin 39A 22rf were available as well, just maybe not as handy. Later a Mini-14 was added to the mix.
We were in no danger from the critters, except maybe snakes in the afternoon. The two legged critters were more of a threat. I'm told that now conditions around the river are more tense. A dozen or so years back, rafters going down the Santa Elena Canyon were occasionally sniped on by folks on the south rim of the Canyon as they rafted the Rio Grande. The more 'remote' you are, the more vulnerable you become. 911 don't work. What's legal and what's prudent might not be the same.
salty.
edited to add P.S.
The previous couple of three stmts have universal applications. Not just for remote campsites.
sd.