First you can reproduce this issue with the ASkinDemo yourself.
Modify the UnitFrameListView so FullDrag is enabled for sListView1.
First try it with disabled skinning Support, Drag and Drop Column2 in front of Column1.
See screenshot 1 for the result.
Not try the same with Skins enabled.
See screenshot 2 for the result, the column data is not moved to the right columns.
This is mandatory function for me and I can't replace TListView with TsListView as long as it is broken.
Please help me 😀