Such a balance was achieved from the turn of the 20th Century to the time that race-baiters began using Confederate history as a racial lightning rod for political gain.
By the end of the Spanish-American War, both North and South once again saw themselves as one nation albeit with local military heroes. By the later 20th Century, U.S. Army had military bases such as Fort Benning and Fort Bragg and U.S. Navy warships such as the USS Stonewall Jackson that were named after Confederate military heroes.
A National Georgraphic Magazine from the early 1940's labelled Robert E. Lee as an "American" hero.
Southerners do not attach "more" value to their ancestors viv a vis modern America than Native Americans attach to their ancestral warriors or Black attach to their own ancestral heroes. That does not make them any less "American".
Try to pulling an American flag down from it's flagpole in front of a bunch of Souterners and try to burn it and see how far you get.
Try telling a bunch of Native Americans that their Indian ancestors that fought against the U.S. Army were uncivilized, murdering savages and see how far you get.
Try telling a bunch of Blacks that the Black Buffalo Soldiers that fought against the Indians were murderers helping to commit genocide on the Indian people and see how far you get.
All groups, will defend their ancestors against attacks that serve no purpose other than to fan the flames of racial and regional hatred that prior generations tried so hard to extinguish.
As I said, these flag and holiday questions are something that Southerners will have to resolve for themselves. Where the rest of us get involved is when the fringe attacks Northerners as servants of tyranny and uphold the Confederacy as a justified rebellion or even as America's last stand against dictatorship. At that point, people who don't have any particular hostility to the Confederacy do get fed up.
Many who wouldn't object to a "they were brave men who thought they were right" approach to the Confederacy, lose sympathy when the message becomes "the South was right! (and the North wrong)." So yes, nobody wants to have their ancestors attacked, and it's only natural that people will take offense, but that doesn't seem to have gotten through to some hard-core Southern nationalist types.
That's the problem with "heritage movements." When they're taken too far, when it's not just a question of the present honoring the past, but of the present surrendering to past vanity, pretentions, conflicts, hostilities, and hatreds, heritage movements end up sowing discord and causing trouble needlessly.