It is ASB that US and CS could be friends after ACW? My timeline will have southern victory, the officer won't lose the sheet in Antietam like TL-191 but totally different alliances in WWI and WWII.
Anything is possible. Factors including the circumstances behind the defeat of the Union; the terms of the final peace treaty which ends the war, assuming there is one; postwar Confederate and U.S. foreign policy and trade relations; and external threats faced by one or both nations, would all play a part in this situation.
I have always thought the scenario where the U.S. and the Confederacy join in World War I right from the beginning, one with the Central Powers and one with the Entente, as one of the less plausible scenarios. Both American republics would have a strong American tradition of isolationist foreign policy, and would be very reluctant to get involved in a European conflict. German submarine warfare would be, as in OTL, the most likely catalyst to draw one or both of them in. Therefore, if both of them enter the war, they most likely both fight on the side of the Allies/Entente.
Of course this is all assuming that World Wars I and II happen at all in such a timeline. In my own
THE BLACK AND THE GRAY timeline, there are a couple of major world conflicts in the early 20th century, but they are not the same conflicts which occurred in OTL. They pit completely different alliance systems against each other, are fought over different issues, and have different outcomes than the OTL World War I and World War II. I think this is much more realistic than the Turtledovesque approach of following OTL almost verbatim and "changing a few of the names to protect the innocent."