If you are legally allowed to carry a weapon in your state, you are now legally allowed to carry a weapon into national parks.
The same rules apply to NPs as the state they are in.
For instance, I live in PA and I have an LTCF (license to carry firearms). Since I can carry concealed in most places in PA, I can also now carry in Valley Forge NP for instance - only not in federal buildings like the welcome center.