For information I have tested a nightly version 8.1.32, and the bug is resolved : I can push tag from EAM to a remote Realtime Provider when "Tag Editing Permission" is not empty.
Edit : but don't think EAM use security Edit define in Realtime Provider. EAM use Service Security configuration
I had the same error in 8.1.43 (EAM and gateway have the same version)
"Failed: Attempt 1: Access Denied. Remote tag editing is not allowed for tag provider 'MES' in the calculated zone."
I did all recommendations in this thread, but it did not work.
Any other thing that I can try ?