Most citizens were pretty happy until the war started. The people of the Republic were immediately disapproving of the war after it started taking heavy resource tolls on the states for what seemed like a flimsy reason to fight in the first place. The states police themselves, so the national government has no hard control over that. The Lunar army does still patrol the continent, but they aren't permanently stationed anywhere and just go where they're needed.
The Empire had pretty good propaganda, so the citizens were very supporting the first half of the war, until the government started tightening its control out of paranoia. The Empire's policing is getting stricter and stricter as of late, with soldiers placed in every major city to stop possible riots and revolts.
Because most of the military fights take place between the continents, people are generally advised not to travel between them for fear of the crossfire. People are scrutinized heavily if they want to travel to the other continent in a legal manner, in case of spies.
Do the people in both sides like their government? Do they have an abusive police force/military? Are citizens allowed to leave their side?