When your Plex Media Server is claimed or signed in to a Plex account, then all access to the server will require authentication by default. That means that you either need to be signed in with the server’s admin/owner account or with an account with which the server is shared.
This helps keep your server, computer, and network safe, because only authorized access is allowed by default.
Related Page: Remote Access and Granting Library Access
In rare cases, you may decide that you wish to allow very specific access from the local network without authentication. You might do this if using a third-party Plex app, which doesn’t support authentication, for instance (though all modern official and third-party apps should already support authentication).
To make an exception, look in your Plex Media Server’s advanced network settings, under Settings > Server > Network > List of IP addresses and networks that are allowed without auth.
Here, you can specify LAN addresses as either a specific IP or a IP/netmask (to specify a range). Separate multiple values by a comma and be sure not to include any whitespace (e.g. spaces).
Warning: Adding exclusions here can potentially impact your server, computer, and network security. This is an advanced setting and you should only do so if you understand the consequences.
Related Page: Network
If you have lost access to the Plex Media Server for whatever reason and need to reset the “List of IP addresses and networks that are allowed without auth”, you can do so manually by editing the allowedNetworks advanced, hidden server preference on the server computer/device. For more details, see the corresponding article.
Related Page: Advanced, Hidden Server Settings