Correct Apple ID and PW, but cannot log into iCloud on Mac

Might be a corrupt .plist.

Do a backup, preferably 2 backups on 2 separate drives.

Quit System Preferences.

Go to Finder and select your user/home folder. With that Finder window as the front window, either select Finder/View/Show View options or go command - J.  When the View options opens, check ’Show Library Folder’. That should make your user library folder visible in your user/home folder.  Select Library. Then go to Preferences/com.apple.systempreferences.plist.  Move the .plist to your desktop.

Restart the computer, open the application, and test. If it works okay, delete the plist from the desktop.

If the application is the same, return the .plist to where you got it from, overwriting the newer one.

Thanks to leonie for some information contained in this.

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. If the log won’t post, try posting it in Pastebin and provide a link in a reply        Pastebin

Etrecheck – System Information

Hello, did you try to start it in safe mode and try it then? Also, did you try signing out of your Apple ID on the MBP, restarting the computer and signing back in?

Contact advisor in apple support see this link https://support.apple.com/en-in/HT201232

Read the article https://support.apple.com/en-in/HT204904

You are welcome.