We updated one of our SDE editor's computers from 10.3.1 to 10.6.1 (ArcGIS Server SDE at 10.3.1). I am able to edit on their 10.6.1 computer, but when they go to edit the same data they get the red warning 'No Editable Layers' with a warning for each layer 'Check to see that you have the appropriate permissions'. We have tested numerous machines both on Windows 8 and 10. We had that user edit the same data on ArcMap 10.3.1 and they were able to edit.
Similar issue - Cannot edit SDE in ArcMap 10.6.1 ?