I have never been happy with the premise that the US & CS would be permament Opponents.
I see the US - CS as closer to OTL's US - Mexico, Not the Best-est Friends, but certainly not Enemies..
Depends on whether or not the Confederates go territory-grabbing in Central America and the Caribbean and this leads to another war with the US - that could really sour relationships for a long time.
(OTOH, if the Confederates tried territory-grabbing and got into a fight with the
British, it could definitely improve US-Confderate relations...British Empire, bullying out fellow americans - some schadenfreude, no doubt, but also sympathy)
The CS would be one of the US's three biggest trade partners. Canada & Mexico being the other two. Not sure of the Order here.
Not sure the US traded that much with Mexico in, say, 1914: backward place, Mexicans still living who remembered the US-Mexican war...
I see the CS being Neutral in GW 1, while having lots of Volunteers in the US AEF..
Again, depends on how the UK and Confederacy get along post-war: if the UK remains the Confederacy's biggest cotton-buyer, and don't, say, slap down Confederate efforts to grab bits of Latin America and/or Africa, they may be pretty pro-UK: given their lack of attraction as a place to emigrate to, they won't have large numbers of recent German immigrants arguing the German case.
In any event, the Confederacy is _not_ going to come in on the German side: they can't do anything to help Germany directly with the British/French blockade in place, and grabbing, say, Jamaica is just going to piss off the UK and possibly the US to no real effect.
Possibility: in this TL, the *Zimmerman Telegram that brings the US into the war is one sent to the Confederacy, offering German support in regaining West Virginia and perhaps Kentucky (heck, the Confederacy would be a more credible ally than poor "too far from God, too close to the United States" Mexico).
In GW 2, I see the CS joining the Allies along with such as Mexico and Brazil, and sending the same division or two, along with being a supply centre.
Given racist attitudes, they might just join the US not long after *Pearl Harbour, if some such incident occured: asiatics attacking the Americas, threatening White People...
Bruce