I've heard people jokingly say, "One side collects guns and the other collects mental disorders."
That's obviously an unfair shot but there's some truth to it.
Left leaning areas tend to be centered around city centers where right leaning areas tend to be rural and control things like shipping and food production.
The police and the military all have a noticeable conservative bend at least at the lower levels.
This wouldn't be a north vs south situation where each side would be roughly equally matched.
In a true right vs left civil war, at least as the politics line up right now, the right faction would win by simply isolating and choking off the cities.