When my id is greyed out while I’m not connected to server , is that cause I’m not connected to Wi-Fi, why is that?

When your Apple ID is greyed out, please check: 

If it is a private iPhone, see -> Use parental controls on your child's iPhone, iPad and iPod touch

Use parental controls on your child's iPhone, iPad and iPod touch – Apple Support (UK)

• 👉 Check restrictions -> tap Settings -> Screen Time -> Content & Privacy -> scroll to Allow Changes.

or

If you have a MDM profile, you need to contact your company - IT department.