Can't turn off screen time as Apple Account logout button is greyed out

This is most of the times happening due to screen time restrictions. Please go to settings>screen time>content and privacy restrictions, and make sure that the button at "allow account changes" is set to on

You can also try and turn off screen time altoegether

When you have done this, you can click on the sign out button

● If an app or feature on your device is not working, not appearing, or is restricted (grayed out), a frequent reason is it may have been disabled using Screen Time, or by an IT administrator if you are using a device owned by an employer or educational institution.

- Read this support article If your Apple ID or other options are greyed out in Settings —> If your Apple Account is grayed out in Settings - Apple Support

Tap Settings > Screen Time > Content & Privacy > scroll to Allow Changes and turn on.

- If the device is managed (Settings > General > VPN & Device Management), contact the IT department that is doing the managing.

● Situation where a VPN was preventing action —> Unable to sign out of my Apple ID on my i… - Apple Community