As a son of the South, I took a lot of pride in some of these kinds of monuments as a kid. In particular, there's a monument to Dick Dowling for the Battle of Bolivar Pass which should never be torn down. Defense of Texas from invaders is always a good thing. Also too, the Alamo, San Jacinto, Goliad, the "Come and Take It" flag from Gonzalez (although it's been profaned).
Likewise, if Virginians like their Robert E. Lee statues, they should be able to keep them. People in Charlottesville didn't like them anymore. It's really nobody else's business at that poont. I'm sure that Lynchburg and plenty of other towns in Virginia are still chock-full of Lee statues and Confederate symbols.
However, everyone should have a gimlet eye for Southern monuments which were erected as symbols of white supremacy during the Jim Crow period and especially post WW2, when, Southern "heritage" was becoming code for white supremacy and their exponents' and their desire to keep darkie down.
General Lee himself is a contradictory figure. Owned slaves, did not want Virginia to secede, but when it did, he followed his state. His plantation in Arlington was seized by the Federal government and turned into a war cemetery for Union soldiers, now known as Arlington National Cemetery. Tequilla referenced "Washington and Lee University." The "Lee" is because he served as the university's president after the Civil War, and his management helped prevent the closure of the institution.
Lee himself did not want Confederate symbology at his funeral, and disapproved of it generally.
Put another way, there's ONE monument to Field Marshal Erwin Rommel in Germany, despite his unquestioned talents as a leader and his opposition to Hitler. That monument is located where Rommel committed suicide rather than face trial by a Nazi kangaroo court.
And yes, the Rebellion of Treason in Defense of Slavery is roughly akin to Nazism on the good<---->bad spectrum. Anyone saying it was about state's rights needs to read the goddam Confederate constitution or the writings of any secessionists.
People in whose states and towns Civil War monuments are located can best decide how and whether they should continue to be displayed. If they are displayed, IMO, they should be accompanied with an interpretive plaque describing the role of slavery in the Confederacy, post-Civil War Reconstruction, Jim Crow, and the Civil Rights movement which helps to illustrate how the monument came to be.
TL;DR- if they like their racist monuments, they can keep them