Confederate soldiers, sailors, and marines that fought in the Civil war were made U.S. Veterans by an act of Congress in 1957, U.S. Public Law 85-425, Sec 410, Approved 23 May, 1958.
This made all Confederate Army/ Navy/ Marine Veterans equal to U.S. Veterans.
Additionally, under U.S. Public Law 810, Approved by the 17th Congress on 26 Feb 1929 the War Department was directed to erect headstones and recognize Confederate grave sites as U.S. War dead grave sites.
Just for the record the last Confederate veteran died in 1958. So, in essence, when you remove a Confederate statue, monument or headstone, you are in fact, removing a statue, monument or head stone of a U.S. VETERAN.