How tarnish? They say they're not ashamed of their ancestor.
Moral degeneracy and indecency? There were many people in history that you might be uncomfortable being descended from, does that make you indecent or a degenerate?
I don't share their sentiments (shame at the monument, guilt over white privilege), but Stonewall Jackson was a convinced Christian and maybe he would.
Maybe he wouldn't have wanted statues of himself put up in the same way that many war heroes don't like to talk about their experiences.
The monuments usually weren't put up by the people they depict.
Sometimes it was those who never saw action who were most devoted to the myths.
I have a very close friend who is a descendent of Nathan Bedford Forrest. (I actually looked into this, and it checks out).
Needless to say, this is a pretty complicated legacy.
The family position seems to be, “He was a brilliant soldier and never intended for the Klan to become what it was. At the same time, his tactics, his cause, and his legacy are not anything we endorse.”