The error 'The layer, [lyrName], cannot be added to the map.' appears when attempting to view a feature layer (not hosted) in the Map Viewer as either Publisher or User in Portal. The same feature layer can be viewed successfully, edited and queried when logged in as administrator. The feature layer is shared with the appropriate groups. The issue does not present itself in ArcGIS Online. The feature layer which the issue was first brought to my attention has a little over 200 features in it, when published it was published with several tables. I'm assuming the root cause is something simple that I've overlooked however, cannot seem narrow it down.
The only solution I found to this issue was to delete the original feature layer and republish it. I'm not sure what caused the service to be view able by admins but not users or publishers however, deleting(not overwriting) and republishing worked to resolve the problem.