Some things to consider:
The soldiers from both wars were conscripted.
Both fought for their country.
Confederates were defending their homes (like the Vietnamese); Americans in Vietnam were the “invaders” not unlike in the Civil War.
No Confederate was tried for treason (only one was convicted of a war crime — falsely).
By an act of Congress nearly 100 years ago all Confederate Veterans are to be considered American Veterans.
All Presidents have since honored Confederate Veterans (even Obama).
Practically none of the conscripted Confederate.
Soldiers owned slaves.
Germany and other nations of Europe honor the German soldiers (not Nazis) that died in WWI & II.
After the Civil War and the Vietnam War both sides have gone to great links to reconcile with each to other and heal the wounds of the past to great success.