Recently New Orleans dismantled a monument to the Battle of Liberty Place, which was a riot in 1874 against racially-integrated politics. The inscription on the monument explicitly mentioned white supremacy.
The monument was not a Civil War monument since the riot in question took place 9 years after. But are there any memorials honoring the Confederate cause located on public land? Since the Confederates were essentially traitors to the Union, it seems improper for the city to honor them with a public monument.
Well I suppose the one important part of your question that is part clarification request and part answer is to ask, "Do you mean anywhere besides battlefields?"
Most of the major battlefields, particular in the Eastern theater are now national parks of one variety or another. And many do have monuments that if not celebrating the Lost Cause, are greatly informed by Southern Historiography and the Lost Cause mythos and are meant to glorify and honor the fighting men of the Confederacy, without any caveats or asterisk about not supporting slavery or anything of the like.
Lets just look at the Granddady of them all in the Gettysburg National Military Park. Virtually every state in the South and many Northern ones have paid for monuments to the troops from their state who fought there, in addition to markers and memorials for individuals and specific units.
For instance Virginia spent nearly a million dollars in 2017 cash to build theirs in the early 1900's. It features General Lee mounted atop a cenotaph with a statue of 7 of his soldiers from different prewar lives below him. It is located along Seminary Ridge near where he was during Pickett's Charge. http://www.gettysburgbattlefieldtours.com/the-virginia-monument/
Meanwhile just to the South is the one from North Carolina. NC's troops suffered the most casualties of any state despite being only the 2nd most numerous. It features a statue of several men including a wounded officer, veteran, and your soldier charging. It also has a stone with this enscription on it: Pic
To the eternal glory of the North Carolina soldiers. Who on this battlefield displayed heroism unsurpassed sacrificing all in sup- port of their cause. Their valorous deeds will be enshrined in the hearts of men long after these transient memorials have crum- bled into dust.
Thirty two North Carolina regiments were in action at Gettysburg July 1,2,3, 1863. One Con- federate soldier in every four who fell here was a North Carolinian.
It was actually designed by Gutzon Borglum who would also contribute to Stone Mountain and also design and oversee the construction of Mount Rushmore.
These are not isolated things either, virtually every battlefield will have similar. In part it is absolutely a reflection of both the sentiments of the state populations, and ascendency of the Lost Cause in public discourse about the war at the time these monuments went up. And about the priorities of those in federal oversight positions that there was no pushback.
I invite you to reflect a bit, and perhaps clarify what you mean by "glorifying the Confederate cause." It's not uncommon for defeated nations to honor their war dead.
Consider, for example, this inscription, on the Confederate memorial that stands on the grounds of the South Carolina state capitol in Columbia:
This monument
perpetuates the memory,
of those who
true to the instincts of their birth,
faithful to the teachings of their fathers,
constant in their love for the state,
died in the performance of their duty:
who have glorified a fallen cause
by the simple manhood of their lives,
the patient endurance of suffering,
and the heroism of death,
and who,
in the dark hours of imprisonment,
in the hopelessness of the hospital,
in the short, sharp agony of the field
found support and consolation
in the belief
that at home they would not be forgotten.