Hi Kmd2001,
Thank you for using Apple Support Communities. I understand you're having difficulty in removing an email account from your iPhone. I'd be happy to provide some insights.
The common reason for an account being greyed out is due to it being a managed device. That could mean that restrictions have been placed on the device in the form of Parental Controls or through device management from a workplace.
I'd recommend taking a look at this resource regarding restrictions: Use parental controls on your child's iPhone, iPad, and iPod touch
Specifically, this section:
"Allow changes to other settings and features
You can allow changes to other settings and features, the same way you can allow changes to privacy settings.
Go to Settings and tap Screen Time.
Tap Content & Privacy Restrictions. If asked, enter your passcode.
Under Allow Changes, select the features or settings you want to allow changes to and choose Allow or Don't Allow.
Here are some features and settings you can allow changes for:
Passcode Changes: Prevent changes to your passcode
Account Changes: Prevent changes to settings for Accounts & Passwords
Cellular Data Changes: Prevent changes to cellular data settings
Volume Limit: Prevent changes to volume settings for safe listening
Do Not Disturb While Driving: Prevent changes to Do Not Disturb While Driving
TV Provider: Prevent changes to TV provider settings
Background App Activities: Prevent changes to whether or not apps run in the background"
Also take a look at this section:
"Businesses and schools often use profiles, which can turn on Restrictions. To find out if your device has a profile, go to Settings > General > Profiles. Contact your administrator or the person who set up the profile for more information."
Thanks and have a great day.