If you see the Get/Set Property menu it means the field cannot except the object you're trying to drag into it. Most likely you're trying to drag a scene object reference into a prefab or template, which is not allowed in unity.
The Get/Set Property menu is the fallback if the Unity does't handle the drop event - but I admit it's a little confusing in this case... If we can detect this situation, I'll add popup instead: Prefabs can't reference scene objects.
