That depends on how you define "community." There were unionists in West Virginia, East Tennessee, Northern Alabama, Northwest Arkansas, Texas and even in Mississippi. There was fighting and partisan activity and repression of Unionists by Confederate authorities. By the war's end, every state except South Carolina had regiments in the Union Army.
Rudulph definition of "civil war" is a little too pat. Surely different regions had their different loyalties in the English or Spanish or Russian Civil Wars. It wasn't a case of everyone going out and shooting at everyone else in every town or village, though at times it may have looked like that. And if you lived in the Border States, no one could have convinced you that there weren't two factions fighting for control of the same governments.
It was not a civil war in those parts of the South removed from the border regions. Had it been a civil war, Lincoln's government could have leveraged local support to subdue those states brutally, as it did in Maryland, Kentucky, Missouri, and West Virginia.
This makes no sense. Lincoln could no more "leverage local support" behind Confederate lines to subdue the rebels than Davis could do so in Southern Illinois or in New York City to securely establish Confederate control there. Once Union authority was reestablished in Tennessee many mountain Unionists who had been persecuted by the Confederate regime were certainly glad of it, though.
Neither habeas corpus nor freedom of the press were ever suspended in the South, even in the most desperate of times. The Raleigh News and Observer wrote after the war "It is to the honour of the Confederate government that no Confederate secretary could touch a bell and send a citizen to prison."
Learn your own history, Rudulph! 4,000 political prisoners held in the CSA.
The governors of Illinois, Indiana, Ohio, Pennsylvania, New Jersey, and New York reported that they could not enforce the draft without 10-20,000 troops in each state.
How about taking a look at the whole picture, North and South? The Governor of Georgia disputed the Confederacy's right to impose a draft and didn't want it to be carried out.
It was because the South still adhered to the transcendence of principle. The South did not believe that the end justified the means.
Nonsense. Whether the issue was slavery or expropriating property or burning down New York, or imposing a draft or suspending habeus corpus or dragging free blacks back to slavery or firing on one's own countrymen or former countrymen, there was no shortage of "end justifies the means" thinking in the old Confederacy.
Look at some of the theories of absolute state sovereignty developed by defenders of the Confederacy, before accusing others of hypocrisy or brutal pragmatism or power worship. For there is enough nihilism and brutal state worship in radical state's rights theories to call such assaults on others into question.