Mob rule doesn't need to occur for a state to leave the union. It can just as easily go out through the processes of the existing republican system of governments in each state. Put differently, the state legislature or a legislative convention can adopt an ordinance of secession and enact it according to the processes of that particular state. State government systems vary in type meaning that some will do it slightly different than others. Some may hold a ratification referendum, some may not. But in each and every case the process can be republican.
What mob rule? The seceding states voted in convention to leave.