The thought of a civil war is VERY messy. My (limited) familiarity is that I’d say 80% of the enlisted tend to be from the poorer (bottom 3-4) deciles of the population. The upper enlisted officers tend to come from families that have been in the services for a long time. They are more from the red/purple areas than deep blue. Officer Corp is more split(again from my very limited experience), Flag officers are VERY political and Obama’s purge of the flag ranks (as well as Col. ready to promote) means there is a very blue tinge at the top. Lower rank officers likely come from families that have traditions of service and come from more traditionally conservative backgrounds as the militery calling is pooh poohed by the Left. Pretty sure neither red nor blue troops would kill civilians without severe provocation. Most would also not participate in massive disarmament of citizens. I think the latter ends up with mutinies and fragging of officers, with enlisted disappearing off into the bush. That said, the Left has its own shock troops in the armed bits and bobs of Antifa/Pantifa and other similar groups. They are far less morally bound than the members of the armed services. Would the National Guard and LEO stand back and let them go at it? Beats me, I’m not eager to find out.
As for strategic resources, the blue states have an issue. I think all the missile bases, plus Whitman AFB (B2, soon B21) are in red states). The Atlantic Boomer base is in a red state (no boomers run out of Groton CT any more), Pacific Boomer base is at Bremerton WA but would that matter? Boomers are odd they really try hard to stay at sea for long periods before switching crews. In a Red/Blue divorce, the Reds end up with most of the fixed ( Missile assets). I doubt the Red would disarm, given the Ukraine precedent.
Honestly any scenario I see tends to be rife with insurgencies. Blue in the more rural parts of Red would have massive hit and run attacks on them by light arms. Red going into citified areas will have Viet Cong like insurgents blending into the populous (with either the populous supporting them or by threatening the populous.
I just can’t create an Arisian like vision of the cosmic all on this one. If I were using the old magic 8 ball I’d be getting “Better ask again” or “Reply Hazy, try again”. The only thing I can say is I deeply doubt your model of a looser coalition, it seems very doubtful. Much of the Blue side views this as almost a theological/eschatological vision. There are as likely to live and let live as the 16th-century Spanish Inquisition. Certainly, there are parts of them that don’t believe (all) their nonsense. But those parts know that if they divert from the path, they are likely to find an ice pick in their forehead like a good menshivik.