"Heritage not hate" is an effort to sanitize the Confederacy, reducing it to military heroism. If one wants to honor a Confederate ancestor or near-ancestor, then that is fine. This in theory is on effort to endorse slavery, racism, or fascist causes such as the Klan. People flying a Confederate flag among banners of Nazi Germany soil whatever connections those admirers of the Confederacy have to any Confederate heritage.
Slavery and racism are disgraces. Fascism is unmitigated evil.
The united heritage of Dixie, which is literally entirely based on origins and has the single most unique culture in the western hemisphere, with a singular worldview wrapped entirely around tradition.
The Southern white tradition from before and during the Civil War is one of the most insipid and undistinguished in history. African-Americans were far more creative in making culture out of the scraps that their masters than were the masters themselves. That's not what people talking about the Confederate heritage talk about. They aren't praising the Black South.
Aside from the great genius of Jefferson, the most interesting part of the white southern heritage was the creative activity of Germans and their offspring in Virginia and North Carolina. But remember -- they were Germans. German lands have a great and glorious culture tradition with the exception of a dozen years of shame.
Cultural pride? In music alone I will take one Dvorak, one Grieg, one Sibelius, or one Bartok over all the musical heritage of the White South before Civil War. There was much cultural creativity in the South after the Civil War -- but that was after the demise of the infamous "Peculiar institution".