Hey, TVproviderHELP.
I see that you're unable to sign out of your TV provider account in the settings on your iPhone. The button is grayed out, and I'm glad to help.
Restart your iPhone, iPad, or iPod touch -- Restart your iPhone. Once it's returned to the Home screen, see if you can disconnect from your TV provider.
How to back up your iPhone, iPad, and iPod touch -- If restarting your iPhone didn't resolve the issue, please be sure to have a fresh backup to keep your personal information safe. In order to back up your Health data, the backup needs to be encrypted. iCloud does this automatically, but iTunes doesn't. If you'd like to use iTunes to back up your iPhone, refer to this article: About encrypted backups in iTunes
If you can't update or restore your iPhone, iPad, or iPod touch -- When an application isn't working as expected, a good step is deleting and reinstalling the app. Since you can't delete the Settings application on your iPhone, I'd like for you to reinstall iOS. The section titled "Put your device in recovery mode and set it up again" will walk you through all the steps to reinstall iOS software on your device. See if you're able to turn it off now.
Let me know how that goes, and take care!