The primary legal issue is when states or localities ban both open and concealed carry, effectively rendering firearms illegal outside the home, and obviating the "bear" portion of the "keep and bear arms" of the Second Amendment. Overly broad open carry restriction are also problematic in areas that permit activities hunting. The recent federal appeals court cases in California, Illinois and elsewhere require that jurisdictions simply permit some type of objectively enforced (i.e., "shall issue," rather than "may issue" carry laws, but certainly do not mandate legal open carry.
Similarly, a great many gun rights supporters not only have no objection to universal background checks, but support it in theory. The devil is in the details. Laws to open-up the NICS system to private parties or similar suggestions would probably be widely supported as pass easily. The objections are to anything that is or could be an effective registration list or when the laws are linked to other controversial measures like magazine limits. Recent incorrect and legally challenged seizures in states like New York have certainly not helped to minimize these objections.
Lastly, I would emphasize that the Second Amendment and state constitutional analogs only set a maximum level of firearm regulation. As you note, there are a multitude of restrictions that are perfectly constitutional. The issue is not the Second Amendment, rather its lack of sufficient political support for restrictions. The Second Amendment can disappear tomorrow, and not much would change.