The Troubles is the archetypal conflict you want to look to. Two sides of ideological retards with complete buy-in murdering each other whilst the federal government desperately tries to keep some semblance of order, but eventually gets accused of collaborating with one side or the other. There will be no pitched battles or even clearly delineated 'territories'. The ideological lines will be districts, streets and even buildings. Life will continue as 'normal' but it will be the new normal of checking your car for explosives before work, constant active shooter drills, people just 'disappearing' on the regular. There will be whole swathes of the country where you wouldn't even know anything was going on. And then other parts that will look like an active warzone.