"Roughly 8,400 active duty servicemembers have been removed for refusing vaccine orders, according to the latest DOD data shared with the DCNF. The Army tallied a 97% vaccination rate as of Dec. 16, but roughly 9,000 soldiers remain unvaccinated."
If it is the same across all services as it was in the Army, only 3% are willing to try to dodge the clot shot. This 3% wouldn't be enough to help in a balkanization scenario. You'd need whole National Guard units to pledge allegiance to your new cause; 3%, even if it was the leaders (it wasn't, they pushed this nonsense) won't be enough to coalesce into a new fighting force.
Source: https://dailycaller.com/2022/12/26/mandate-overturned-unvaccinated-troops-risk-reprisal/
Outside right-wing fantasy fiction, nobody believes "DA TROOPZ" are going to join in some populist uprising, whether or not some of them refused the clot-shot.
Go ahead, someone: Post an instance of a single US military unit refusing an order to engage US citizens, ever.
On the other hand there are abundant examples of the opposite. Here are a couple:
George S. Patton, Dwight Eisenhower and Douglas MacArthur "cleaned up" the Bonus Army. No record of desertions in those units. This probably had a great influence on the sheep-like behavior of the "greatest generation" when they were told to turn their gold over to the government.
Also, under Billy Mitchell the US Army Air Corps flew top-cover and surveillance for a corrupt sheriff who engaged in aerial chemical warfare on civilians with his "private air force". President Warren Harding then sent troops to disarm the "treasonous" coal miners.
Very few examples of the US military ever being ordered to be against US civilians to draw from, making conclusions on few data points is tenuous.
However, I can give you a big example to counter your narrative, where you appear to allege that the military could NEVER break apart and go to both sides. 1861-1865.
Plenty of folks believe that since the deck plate military is primarily working class and southern, that they'd join the good guys in a balkanization scenario. I'm doubting it will happen, based on vax status.
Do you believe that, without conscription, the demographics of the US military will continue to be sufficiently "working-class and Southern" for long?
Now there's a rub, because I firmly believe that this country is already set against itself to the point where support for only two identifiable 'sides' (as in Civil War I) is impossible.
Try it yourself: Assemble the following factions, belief-systems and "movements" into anything resembling the 1860s alignment: two compact, unified belligerent forces, that held an identifiable land-mass with interior supply-lines:
I think it's far more likely the US.gov will collapse to the point where it can no longer control the territory. You'll know that's occurred when those troops' paychecks start bouncing or are converted to some digital Zimbabwe-scrip. THEN you'll see whole units deserting and setting up fiefdoms, and a short period of "Mad Max" anarchy.
But once the formerly-united-States falls below the critical mass necessary to repel invaders, a long line of older, harder cultures with centuries-old grudges will move in to pick up the pieces.
You took the ball and ran with it.
I make one conclusion based on one solid piece of evidence, that with 97% vax status it means that military is not gonna side with the good guys (it was a hypothesis really) and you build an entire superstructure on other conclusions, some of which are based on conjecture.
You're welcome to them.