When presidents still had some common sense and integrity…

Confederate veterans were afforded status equal to that of United States veterans by an act approved by the Congress of the United States of America on May 23, 1958, and signed into law by President Dwight D. Eisenhower, in accordance with Public Law 85-425, thereby amending the Veterans' Benefit Act of 1957 

US Law that defines status of Confederate Veterans 
Public Law 85-425 adopted May 23, 1958 as H.R. 358 

To increase the monthly rates of pension payable to widows and former widows of deceased veterans of the Spanish-American War, Civil War, Indian War, and Mexican War, and provide pensions to widows of veterans who served in the military or naval forces of the Confederate States of America during the Civil War... 

CONFEDERATE FORCES VETERANS 
Sec. 410. The Administrator shall pay to each person who served in the military or naval forces of the Confederate States of America during the Civil War a monthly pension in the same amounts and subject to the same conditions as would have been applicable to such... if such forces had been service in the military or naval service of the United States. 

Sec. 2. This act shall be effective from the first day of the second calendar month following its enactment.