Would it be legal for governors to send National Guard to protect recruiting stations and other unarmed military?
I do not believe that would be a good idea. It would negatively impact recruiting efforts and send the wrong message to the public. My suggestion would be to arm the SNCOIC, which every RS has. This individual is typically not a canvasing recruiter and is on-site the majority of the time. Further, having a senior NCO or SNCO armed at random would benefit the overall security as any potential shooter would not know how many armed uniforms would be on-site. Canvasing recruiters could carry (secured) weapons in their POVs as they visit residences and schools.
Great question!
I don't know the answer. But, I could imagine that the NG could be told to secure and patrol the general area where the stations are located, even if posting them right at the recruiting area was somehow forbidden.
Federal recruiting centers are federal proper so national guard troops, unless they are federalized, would not be allowed to carry inside a federal center. If their center was on federal property, they couldn’t even bring a weapon onto the federal grounds so they would have no means to protect themselves driving to and from work.