You won’t be able to sign-in to your device, use iMessage, iCloud and other Apple related services, if the Apple ID is greyed out or become unresponsive on your iPhone.
In general, the most common reason for Apple ID being greyed out on iPhone is due to passcode and account changes being disabled on your device.
Apart from this, Apple ID can also become greyed out due to repeated incorrect password attempts, problem with Apple’s iCloud services and other reasons.
Fix Greyed Out Apple ID on iPhone
Before going with the troubleshooting steps, it is recommended that you Power-off your iPhone > wait for 30 seconds and Restart the device.
This can help, if the problem is being caused by a stuck app or process preventing access to Apple ID.
If the Apple ID is still greyed out or not working, you should be able to fix the problem using troubleshooting steps as provided below in this guide.
1. Disable Restrictions on Account Changes
As mentioned above, the most common reason for Apple ID being greyed out on iPhone is due to Account changes being locked on your device.
1. Go to Settings > Screen Time > Content & Privacy Restrictions.

2. On the next screen, scroll down and tap on Account Changes.

3. On the next screen, select the Allow option.

2. Disable Restrictions on Passcode Changes
Similarly, the problem could be due to restrictions placed on Passcode changes on your device.
1. Go to Settings > Screen Time > Content & Privacy Restrictions.

2. On the next screen, scroll down and tap on Passcode Changes.

3. On the next screen, select the Allow option.

3. Disable All Content & Privacy Restrictions
If the problem is still persisting, you can disable all Restrictions on your device and see of this helps in fixing the problem.
1. Go to Settings > Screen Time > Content & Privacy Restrictions.

2. On the next screen, move the toggle next to Content & Privacy Restrictions to OFF position.

This will disable all types of content & privacy restrictions on your device.
4. Disable VPN
If you are using VPN, disable the VPN service on your iPhone and see if this helps in fixing the issue.
1. Open Settings > scroll down and tap on VPN.
2. On the VPN screen, move the toggle next to Status to OFF position.
After disabling VPN, you should be able to access the Apple ID on your iPhone.
5. Family Sharing Settings
If your Apple ID is included in family sharing, only the parent account will be allowed to access Apple ID. The only fix in this case is to remove your Apple ID from Family Sharing.