Chances68
Confederacy and Union are more accurate and scholarly titles.
All hat
If you are using them to identify a group of people, or a political movement, etc., then they are proper nouns. If you are using them only to indicate direction, "the army moved north", then they are common.
Mercy
proper in that connotation
Anonymous
Royalists and Parliamentarians would be more appropriate. The Civil War was not divided on North/South lines so it is meaningless to use those terms.