To agree that the southern states had the right to leave the union is not to support slavery or out of racial prejudice as many detractors contend, they do that either out of ignorance or to maliciously obfuscate from the facts of the matter. Many conservatives today see all the evils in this country all as the result of FDR but the trouble goes back much further, the country as set up by the founders was dealt a death blow by Lincoln. His success was the beginning of the centralized state and the decline of freedom as well as the birth of corporate welfare and the insidious relationship between big business and government. Of course many conservatives excuse the wrongs of the War Between the States because of its success at keeping the union together which they see as the greatest good. These people have a loyalty to the concept of nation and geography over the love of liberty. The idea of support for the south goes to the concept of liberty and self determination not that the south was correct in the make up of its society. Of course many conservatives defend Lincoln because they are loyal Republicans and see the party as representing limited government, they fail to see how the Republicans started out as the party of big government. BTW my grandfather's grandfather lost a leg fighting with the Union forces. My grandfather used to tell me how his grandfather had to sit down on the floor and shimmy down staircases.
P.S. The "Civil War" as you call it is a misnomer. A civil war by definition is when two or more groups vie for the sole control of the government of a country. The south seceded from the Union so a more correct name for the war could be the war between the states though I prefer The War of Northern Aggression myself. "Civil War" is more propaganda put forward by the winners so we could feel better about ourselves.