The state cannot prohibit the people from keeping and bearing arms so as to deprive the United States of their power to call forth the Militia. The state could insist that citizen's arms be kept in the state armory. The state could supply arms to be used in training.
Keep in mind that the federal government has the power to "provide for organizing, arming, and disciplining the Militia".
And even there federal action would be necessary. The nutjobs wouldn't be able to go to court in the name of Congress.