Airport LOg in

Based on the information in your post, it sounds like your Mac is running the Mojave operating system.

If that is the case, you might not be aware that Apple dropped support for Back to My Mac in Mojave, so the BtMM settings in AirPort Utility need to be deleted to get things to return to normal operation. More info here:

Prepare for changes to Back to My Mac - Apple Supporthttps://support.apple.com/en-us/HT208922

Open AirPort Utility, select your AirPort, and click on the Edit button in the smaller window that appears

Click the Base Station tab at the top of the next window

Click the - (minus) button at the bottom of the Back to My Mac list to delete the entry for your Mac there

Click the Update button at the lower right of the window to save the new settings and give the Airport a minute to restart

The Apple ID will NOT be recognized if you have Mojave installed on your Mac and you have enabled Back to My Mac in AirPort Utility.

To confirm this another way......

Open System Preferences (the gear icon on the dock)

Open iCloud

You will not see any settings for Back to My Mac......because Mojave does not support Back to My Mac. So, you cannot enter your Apple ID for a feature that is no longer supported in Mojave.

If that is the case, delete the Back to My Mac settings, as that is the only "fix" for this issue.

The link to the Apple Support document explains all of this. Contact Apple Support directly if you continue to have problems with this.

Please contact Apple directly. We are users......just like you.....and we cannot help on decisions that Apple has made.