Well, it depends.
People don't fight other people. Political entities fight other political entities for political or economic reasons.
Soldiers simply fight to defend their homes and families. With some exceptions, soldiers are the greatest victims of war.
I'm opposed to monuments that celebrate the Confederacy itself. The Confederacy existed and went to war for the simple economic reason of defending slavery. This historical revisionism about state's rights is bunk. The only state's right they cared about was the right to keep slavery legal.
As for monuments memorializing the soldiers that fought for their homes and families, such as those at Gettysburg, those I'm inclined to accept.
Does this includes statues of Confederate Generals such as Robert E. Lee? Yes it does. Does it include the carvings at Stone Mountain Georgia? No it doesn't. Because in addition to Lee and Stonewall Jackson the carving includes Jefferson Davis. Davis wasn't a soldier but the top of the political structure of the Confederacy.
What do I base this on?
First, because on Christmas Day 1868 President Johnson extended full amnesty to Confederate soldiers and restored to them full citizenship rights. He didn't make an exception for officers.
Second, in 1958 Congress passed Public Law 85-425 related to the pension rate for the widows of veterans. This law defined "veteran" for the purposes of the law to include "a person who served in the military or naval forces of the Confederate States of America during the Civil War…”
Also in 1958, Congress passed Public Law 85-811 dealing with the procurement of headstones for veterans. This law stated “That the Secretary of the Army is authorized and directed to furnish, when requested, appropriate Government headstones or markers at the expense of the United States for the unmarked graves of the following…” The first category listed is “Soldiers of the Union and Confederate Armies of the Civil War.”
In neither of these two laws does Congress make an exception for officers, high ranking or otherwise.
So while Congress never specifically declared that soldiers of the Confederacy are US veterans, the implication of these two laws is that they should be considered as such.