It would be great if the active account/profile in plex was able to be tied to the active user on the Apple TV itself.
A brute force way to do this would be to save all plex settings per Apple user and to use automatic login per account. This would be less than ideal as it would require signing in multiple times upon initial setup.
More integrated options would associate only the active profile with the active Apple TV user but share a single account
See Apple’s guidance for reference
Customize your app for each user on Apple tv