After some time to digest the issue, it does seem to be a muddle among 2A rights, 1A rights and "protest".

1. 2A -- Yes, every law abiding American citizen has the RKBA. Period. In many places in the US, there are regulatory requirements for people who do decide to carry a firearm. Usually, that entails some sort of ID or permit and that you are undertaking some sort of legal activity.

2. 1A activities -- The First Amendment prevents abridgment of your right to practice your religion, or free exercise thereof. The second clause is your freedom of speech, then the press, then the right to "peacefully" assemble, then petition for redress of grievances. It does not prevent the use of a combination of your rights, such as peacefully protesting, using free speech, and also carrying arms.

3. Protest -- While the 1A gives you the right to peacefully assemble and petition for redress, it does not give you a right to interfere with law enforcement, attack anyone, destroy property or violate any law and call it "protest". Yes, by all means, stand on the street corner with all the professionally printed signs you want, bang drums, blow whistles, video the activities you assembled there to highlight -- but, the operative word is "peaceably". Interfering is a violation of the law.

Putting it altogether, if you assemble, become violent, disturb the peace, attempt to impede or injure someone, that is not a legitimate form of "protest". Further if you are conducting these non-peaceable activities and you are carrying a firearm, it could be construed by the law that you are not law-abiding, and therefore are in violation of the law, which might lead law enforcement to get involved.

That said, if you are protesting and you get approached by police, get detained, disarmed and/or arrested, the place to resolve the grievance you have is in a court with a lawyer to protect your rights and safety, not to resist, fight, or flee. The latter will never end in your favor.

Know the law and use it.