History is a thing.
Thank the NRA for this myth that any regulation is some sort of Constitutional crisis. I am all for responsible ownership, with the key word being “responsible.” Guns simply do not belong in some situations. Confrontational protests is one of them. Fine, if you want to march an carry signs and guns, fine. If you want to take bullhorns and yell obscenities, that is not a situation where guns need to be present. This could be treated as a limit on right to assembly as well, which also is not absolute. Lay out the plan, and protest. Guns, or anger, but not both.
Even police have strict regulations concerning carrying a firearm, which is why drinking on duty is never acceptable to any degree.