Plex server on Windows 7 machine will not allow browsing using loopback url

What probably happens is that you have required ‘Secure Connections’ on the server.
But when you are using the local address, there is no valid TLS certificate available.
You need to:

  1. tell Plex Web that it is OK to fall back to unencrypted connections when you are in the same local network as the server
    Settings - Web - General - ‘Allow Fallback to Insecure Connections’ = ‘On same network as server’

  2. tell your router to allow ‘DNS rebinding’ for subdomains of the plex.direct domain
    https://support.plex.tv/hc/en-us/articles/206225077-How-to-Use-Secure-Server-Connections

  3. tell your router to use Google’s public DNS servers (8.8.8.8 + 8.8.4.4) because some ISPs DNS servers cannot resolve the .direct TLD reliably

If you cannot achieve 2) and/or 3) you may have to disable ‘Secure Connections’ (or set them at least back to ‘Preferred’)
(Settings - Server - Network)
(restart Plex server after changing this preference)