In NC it is ALREADY illegal to carry a firearm if you are participating in a parade, demonstration, or picket.
Then why did they not arrest everyone at Guilford Courthouse NP? NC laws apply in National parks. The reason is, it's not actually illegal to carry during any and all demonstrations.
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§ 14‑277.2. Weapons at parades, etc., prohibited.
(a) It shall be unlawful for any person participating in, affiliated with, or present as
1-a spectator at any parade,
2- funeral procession,
3- picket line, or
4- demonstration upon any private health care facility or upon any public place owned or under the control of the State or any of its political subdivisions to willfully or intentionally possess or have immediate access to any dangerous weapon.
Violation of this subsection shall be a Class 1 misdemeanor. It shall be presumed that any rifle or gun carried on a rack in a pickup truck at a holiday parade or in a funeral procession does not violate the terms of this act.
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Protest on private property or non state, city, or county owned property and you should be OK. Might be tough to find a place that fits those criteria. But undoubtedly national parks fit it, and I would imagine so does private property. And now for the obligatory IANAL, YMMV, it's your rear on the line so make your own decision.
Also, cities cannot make ANY laws regarding CC that go above state law.
14‑415.23. Statewide uniformity.
It is the intent of the General Assembly to prescribe a uniform system for the regulation of legally carrying a concealed handgun. To insure uniformity, no political subdivisions, boards, or agencies of the State nor any county, city, municipality, municipal corporation, town, township, village, nor any department or agency thereof, may enact ordinances, rules, or regulations concerning legally carrying a concealed handgun. .........
http://www.ncleg.net/EnactedLegislation/Statutes/HTML/BySection/Chapter_14/GS_14-415.23.html