The next US civil war will not be that cut and dried for allies and enemies. The wars within the wars as a concept is accurate even if I disagree with the groupings. All politics is local as the saying goes and war is just a continuation of politics with the niceties stripped away. We might already be in a cold war version of a civil war with riots being the closest thing to battlefields we will see. Once the civil war goes hot and actual combat ramps up the first battles will be fought within the military itself. I cannot imagine any unit larger than 100 people (1/2 of a typical "company" level unit) being ideologically homogeneous enough to function. If the SHTF so hard and sudden that the military is actually needed to quell a riot or rebellion it will be too late. Even if there isn't open mutiny and sedition taking place there will be enough sympathisers to stealthily sabotage whichever side is dominant enough rendering that unit useless.