Just suppose that the Civil War ends with a Confederate victory. Then suppose that during the 1870s, the two American governments agree to reconciliation of their differences. Slavery in the Southern states ends by means of gradual emancipation (as it did in most of the the Northern states) or government compensation, as it did in Great Britain. U.S. history then resumes its course, minus Appomattox, Reconstruction and President U.S. Grant, northeastern states resume a position of political and economic dominance they held nationally well into the 20th century.
The English Civil War ended with similar results. Cromwell won the war, but became a pariah following the restoration of the Stuart monarchy. His body exhumed, Cromwell was beheaded and his skull placed on the end of a pike like a common criminal.
If you like Monty Python, here's a brief tour of the English Civil War --
In this situation, perceptions of our past are likely to change. Even with a Southern victory, following restoration of the U.S. government, Jefferson Davis might have been perceived as a 'rebel' leader. Perhaps Lincoln would not be venerated by the Northern public, and the Northern public would be far less supportive of monuments commemorating their defeat in a bloody civil war that need not have taken place.