If I can regress to topic of helmets. I always thought it would make sense for Confederate soldiers to wear the 1915 Brodie helmet because so much of their kit would need to come from British factories. (Realistically speaking, the South faced enormous political hurdles to industrialization. I feel that Turtledove was far too generous, and far too generic, when it came to Southern industry and war products.)
For the United States, the descriptions in the text (read so long ago that I can no longer think where to find them) reminded me of the Zuckerman helmet, with its tall steeple; a metal top hat; or a conical steel hat with brim. One consideration is that losing the Civil War would have probably doomed West Point as the institution that had incubated treason. This would cripple the Regular Army and create even more dependence upon state militias and the United States Volunteers, in turn producing a very uneven standard of kit. While American industry would be more than up to the task of supplying such a diversity, I wouldn’t expect a fully uniform appearance for Federal forces even by the early twentieth century—and that’s still assuming that the notion of a professional military school took hold again after the defeats of the 1880s.
Out West, probably many soldiers would be issued slouch hats and khaki. The long-running conflicts with Native Americans and Mormons, not to mention inevitable cross-border skirmishing, would probably lead to a soldier with an appearance much different than the “peacock militia” on the East Coast, where uniform articles would be chosen for style, not comfort or battlefield utility. I assume Confederate association with filibusters and the occupation of Cuba would result in their use of cork helmets for service in tropical climes.
Given the border problems, expect dragoons and mounted rifles to slide back out from under the thumb of a generalized cavalry corps. That brings back orange and dark-green braid, along with an opportunity for some gorgeous parade uniforms.
Think about the impact on the Great Lakes if the United States and Canada were to remain at odds well past the Civil War. Rather than cooperate, each nation would probably have build its own set of canals. As during the War of 1812, expect a naval race, along with enthusiasm for the kinds of coastal battleships popular in Scandinavia for Baltic service during the Interwar Period. Just to stake out the differences, the Union would probably retain blue and white as their service colors, while the Confederates replace white with blue-gray.
The Confederacy would probably opt for a cruiser-heavy order of battle, leaving construction of battlewagons to the British and French. The purpose of this fleet would be to conduct commerce raiding. As during the Civil War, I do see the South leaning heavily on new invention, including submarines, aeroplanes, airships, and aircraft carriers.