When launching Plex for Android TV the account selection screen should be shown first, then the selected account’s library.
Android TV is a communal experience with children and adults using it, therefore to keep it segregated the account selection screen should be shown first. This is in-line with other apps such as Netflix, Amazon Prime, etc.
If you go to Settings, under “Account,” you’ll find a setting called “Sign in automatically.” If that setting is off, it will do what you want.
Amending beckfield’s response:
From https://support.plex.tv/articles/settings-android-tv/
Sign in automatically
If you’re in a Plex Home, you can use this option to have the app automatically sign in to the currently-selected user and bypass any PIN for that user.
Unless you checked that box, you’ll be asked to pick a user and enter their PIN when opening the app. Therefore working as requested/described/designed – that makes this less of a feature suggestion 
If it’s not working for you, we’ll need to check if there’s a bug.
2021 clean-up: considering this to be implemented (see link above); no follow-up to verify if there might be a bug involved
