Here in Utah, we have more national parks then any other state so this issue a big concern. We also have millions of acres of monuments, state parks, and federally managed land besides the national parks and every one of them has slightly different rules. In traversing this state, you are bound to enter Federally managed land sooner rather than later. If you are out hunting or shooting and cross over an imaginary line in the sand, you had better know how to deal with it.
I have learned that any problems inside a park will basically boil down to the chief park ranger on duty that day. Some are gun friendly and some are not.
My grandpa routinely took his Glock into Capitol Reef National Park when staying in his travel trailer inside the park campground. I recall him telling me once that he was asked at the gate if he had a firearm. He replied that he did and the ranger insisted it not be kept in the trailer but must be stored inside his truck disassembled. What good is that gonna do you if someone tries to break into your trailer in the middle of the night?! Well, the next year on his trip to the park, my grandpa told the new ranger at the gate he had a Glock for protection and he was going to store it in the trailer or go to the Koa outside the park to stay. The ranger said it was not a problem and let him into the park campground without any questions asked.
Anyhow, it will be nice to uniform all the gun laws regarding national parks so we will actually know what we can and can't do. Capitol Reef and most all the other national parks in Utah are pretty safe and well patrolled but places like Denali in Alaska are remote, full of grizzly, and I wouldn't be happy to surrender my firearm at the gate for anybody. Like grit says, when dealing with your life, I'd rather be fined than found in a grizzly bears stomach.
If it's not far, it's boring.