I recently installed Plex, this is the first annoying issue I discovered, PLEX + TLS + Chromecast = problems. For my case, it leads to an error in the logs "WARN - [Chromecast] Media element error code: 2" and an error message in my screen "There was a problem playing this item". It happens randomly, it can play for 5mins or 40 mins but it will error out always.
Disabling security completely allows for uninterrupted playback without errors but of course security goes down the drain. So many months and these issues still persist apparently.
Yeah, it so depressing ;D
So what I did is opted out of signing in altogether since I don't need to access Plex outside my home network...
Just a tip, if you're like me and don't need to use Plex outside your home network and sign out of plex also uncheck Enable local network discovery (GDM) in Settings > Network and just to be on the safe side uncheck Enable the DLNA server in Settings DLNA.
This way, I feel, and I could be wrong, that your plex media server cannot be pinged from outside your home network, of course that means you have to manually connect your plex media server (for iOS and Android apps that you use to cast) using your plex media server IP address (that is probably set vis your router based on your PMS mac address)
Sigh thats the best I could come up with as far as security goes!