The state of New Mexico has preemption over firearm regulations. Tribes on Native American reservations are not subject to state preemption.
This law restricts any political subdivision of the state's ability to create firearm restrictions of their own. Most states have total preemption which means townships, counties, municipalities, etc. Can not create their own gun restrictions. Some states allow these areas to have preemption on certain things, such as the discharge of firearms. They may also be technically allowed to create firearm laws, but they must be identical in both restriction and penalty to the states law. Certain states have grandfathered in laws that were already in place before the state was preempted.