We haven't heard of that issue since the 6.5.3 release, but will try to investigate further. Knowing that the Always Import setting gets rid of the problem helps narrow things down.
As to the message itself, it's not a real error and something that can be ignored. Warnings are for us developers to let us know something isn't quite right, also not going to break everything. If you go to the Joomla -> Global Configuration area and set "Error Reporting" to "None" or "System Default" it should hide that warning and you can re-enable profile import.