From a few books I read recently about union loyalists in Northwest Arkansas, basically stated they more or less kept their true feeling to themselves and their family. In public, they would inactively support the Confederacy and generally not speak too negatively of it, but at home would encourage their families to remain loyal to the US government. Loyalists were often arrested and jailed, usually for a short time. But sometimes, they were physically abused or killed. One story from the book said a prominent citizen in a city in Northwest Arkansas, who publicly supported the Confederacy, gathered his family inside their house on July 4, 1861, closed all the doors and windows and his whole family pledged allegiance to the United States. Other than pretending to be a Confederate supporter, the mostly just kept their heads down, but that wasn't so easy in places like Arkansas and Missouri.

As far as abolitionists in the south, that would have been extremely dangerous to remain there. If you were an abolitionist in the south, you never would have made it public. You would have been arrested and imprisoned at best.