I popped my head into the forums to ask this question and immediately saw that someone else had already asked the same question. I signed in to reply in solidarity, only to find that it seems the mods have deleted the thread.
This is a really important problem that needs addressing, in my opinion.
Why have changes been made so that I can no longer access my local server directly when plex.tv is down? When was this change made and why?
Excuse me, I’ve just noticed that the thread was moved, not deleted.
But the question stands!
It’s so exciting to lose features every year! /sarcasm
Just no answer at all from Plex staff?
Well, this all leaves a really ■■■■■■ taste in my mouth and makes me question why the hell I’m giving you money every month 
user authentication and also Plex Home managed users authentication is through plex.tv
The requirement to authenticate on the local network and localhost came in August 2016
The other dependency on the internet relates to secure connections which make use of a secure https plex.direct url route to the server and that would need DNS.
Secure Connections came in June 2015
See this support article which summarises the dependencies on having an internet connection
https://support.plex.tv/articles/200484903-internet-and-network-requirements/
No authentication would be required if the server is not signed in to plex.tv and is on the same network as the client apps
Secure Connections would not be used then and there would be no Plex Home users
Sorry that my response is in multiple posts - the plex client apps do cache credentials and it is possible to continue to use the apps when plex.tv is down
Plex Home user switching would need access to plex.tv
There are at least 6 or 7 threads discussing the same issue and the answer is the same. Change the “Secure connections” option in the server to preferred (or off if you do not use remote access) and set the client(s) to allow insecure connections “On same network” and you should have local access regardless of the state of Plex.tv or even without internet.
I know that even during extended outages I have never lost my ability to play my media/
Also you can use “AddressOfPlexServer:32400/web/” to access the server itself from a browser on any computer on you network.
