Unable to sign out of Apple Account

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.

Have you checked at Settings > Screen Time > Content & Privacy Restrictions > Account Changes?