cant log in or out of icloud

Try quitting System Preferences, restart the computer, and the open System Preferences/iCloud to see if you can sign in.

Try setting up another admin user account to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account

Safe Mode - About

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor. Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown.

Etrecheck – System Information

See this article If you can't connect to the App Store, iTunes Store, or Apple Books - Apple Support

Same issue here. This is the second time this has happened since I started using iCloud to backup documents/photos 3 months ago. I can't remember the last time Google had crippling server issues......

I believe some of apples servers are having issues.

Apple - Support - System Status

Try restarting/resetting the router.

I have had the problem since around 10am CST this morning. I cannot connect on my Macbook Air or on my Windows work machine (earlier today). No solution has worked.