https://www.everycrsreport.com/reports/IN10313.html
This is interesting, it explains how national cemeteries deal with the topic. I have seen circle shaped, metal grave markers denoting Civil War veterans. I would never, ever remove a flag from a grave, even though I find this particular flag to be so much more than offensive. I think that Congress has declared them to be American veterans, even if they were traitors to the USA who committed treason. I would guess many who were killed had been duped into their lost cause, similar to the rah rah patriotic propoganda we are experiencing today.