Sovernity was a providence of the State. Sovernity did not reside with the county, or a city, or an individual. As the state went, so did the resident whether they wanted to or not. If you were a resident of Tennessee you were "expected" to be a part of its Militia. If you crossed the Ohio River and joined the Union Army you were a traitor to the State of Tennessee. And likewise the opposite was true.
You could disagree with the political opinions at the early outset the war, but only so long as there was only a need for just a Volunteer army. Once conscription laws were passed that limited ability to express an opposition opinion on either side forever went away. But even in the early stages where open opposition, such as the southern peace societies, to the common opinions of the majority were expressed, committees were appointed to by state authorities to handle those who disagreed. In some cases those Peace societies in the South, were arrested and given choices of either joining the army, or going to prison. They drew the lines pretty closely about this thing of whether or not the individual had the right to protest their government objectives or not. And whether or not free speech gave aid and comfort to the enemy.
While you pointed out the southern dissidents in NW Arkansas and east Tennessee, I would like to also point the actions of Abraham Lincoln and the United States Government in how they handle the secessionist sentiments of the city of Baltimore, MD, and the state of Delaware, Missouri and Kentucky. Along with, later in the war, citizens like Clement L. Vanlandingham and other northern democrats who opposed Lincoln and were outspoken. They were most of the time illegally placed under marshall law, arrested and placed in jails for disagreeing with their governments also.