The Armed Forces of Desert
"Standard" Desert Infantry field uniform. When the Mormons rose up again in 1941, they tore up the railroads and captured US Army men moving from the West Coast through Utah towards Ohio. When they captured them, the Mormons stripped the men of their uniforms, and dyed them to distinguish them from the US. They dyed the uniforms a shade of green dubbed "olive-drab". Despite the fact that this was supposed to be the standard field uniform, there weren't enough captured uniforms to go around, and the Mormons had more important things to make than uniforms, like guns and bullets. Thus, most of the infantry wore whatever home-spun clothes they had when they joined the army.
The standard Mormon helmet, painted a lighter shade of olive-drab. Before the Mormons rose up again, agents conversed with the CSA to see what help they would be. The Confederated were more than eager to hurt the US, and granted the Mormons with old bolt-action Tredegars (they weren't about to waste the new automatic Tredegars as they needed them in Ohio), and piles and piles pf the new helmets that the CS Army used. They were painted a lighter shade of olive-drab.
Since the Mormons raided the US arsenals in the state, the Springfield was their most numerous weapon.
The Tredegar was the second most numerous rifle the Mormons had, as the CSA gave them plenty.
Although the Mormons tried to settle on either the Springfield or Tredegar as their standard infantry rifle, the amount of different guns carried by the men, women, and even children made that impossible. So did trying to keep them all supplied with ammunition. This was one of the Mormons' greatest weaknesses, they had too many guns and too many calibers to keep track off.
The Mormon's main machine gun, the Maxim Mg 08. Seizing the army stockpiles gave the Mormons many of these guns, and they used them to deadly effect.
The Browning Automatic Rifle, or BAR, is an oddity in gun history. Not quite an assault rifle, not quite a light machine gun. Mormon factories didn't make many of these guns, only 100. The man behind the gun, John Moses Browning, a prominent Mormon gunsmith was killed by an artillery shell in 1916 during the US barrage of Ogden. His son, Val Allen Browning, survived the first uprising and found and safe-guarded the plans of the gun. After the second uprising started, he gave the plans to the leaders, who in turn gave the plans to the factories. Despite the fact that not many guns were made, the BAR was very useful in both attack and defense. Val Allen Browning was killed trying to lead a counterattack to push the US away from the Temple. He was carrying a BAR.
Mormon "Featherston Fizzes" used with deadly effect to get rid of US barrels.
The standard plane of the Desert "Bomber Force". The so-called Bomber Force was 10 Curtiss JN-4 “Jenny" biplanes that previously been used as crop-dusters. The pilots would fly in low over US positions behind the front and drop homemade bombs on them. All in all, these raids were pinpricks to the US forces in Utah, and didn't do much damage. In response, the US used their bombers to pound the everloving shit out of Utah cities still in Mormon hands.
This all seems pretty reasonable and pretty likely to me! The Mormons would likely use all kinds of captured US equipment and a hodgepodge of smuggled Confederate arms spliced with more homemade guns and bombs. The more modern US equipment would likely be looted off the battlefield and from soldiers as needed. Older equipment would make up the vast majority of the weapons the Mormons would have.
I think the only iffy thing about this would be the Mormons having a makeshift "air force" or "bomber force". Granted, you choose outdated civilian biplanes and and converted crop-dusters, with the total number only reaching to just 10 total aircraft. I think an explanation as to how exactly they come to get them wold be nice. So its not like the Mormons are ever able to field a force capable of ever squaring off against the US Air Force in the skies, which is a good move. I'd say these planes would be used strictly for night attacks to harass the US troops on the ground.