Hello dchapdel,
Thanks for reaching out through the Apple Support Communities about that difficulty with signing out of your Apple ID on your MacBook Pro.
Are you able to sign into the iCloud website without any issues? iCloud
Have you experienced this behavior with multiple Wi-Fi networks?
Does that persist after restarting your Mac? Shut down or restart your Mac
How about if you boot your Mac into safe mode per the steps in this article? How to use safe mode on your Mac
It can take a few extra minutes to boot into safe mode. Your screen may flash or flicker while in safe mode. Those behaviors are expected. Booting into safe mode runs a check on your disk, and can help isolate conflicts with startup items. Once you’ve tested that, you can restart to leave safe mode.
Should that behavior still persist, you’ll want to reach out to Apple Support so they can look into this further: Contact Apple Support
Take care.