Solution: if you get the "Unsupported AppleID" dialogue following an OS update in OS X on a desktop / laptop.
1) click "Cancel" button in the dialogue box,
then quickly
2) switch to the main Preference window ( button in menu bar that looks like several rows of tiny icons)
3) select the Security & Privacy Preference Pane, go to the Firewall tab and switch the firewall to OFF. (if necessary unlock padlock using your desktop keychain password)
4) re-open the iCloud Preference Pane where everything should be normal again. Login to iCloud if required.
5) switch back to Security & Privacy Preference Pane and switch Firewall back ON.
The above
Worked following "unsupported AppleID" dialogue blocked new agreement in the iCloud Preference Pane following upgrade to Yosemite 10.10.3. (March 2015)
I'm not sure which aspect of the Firewall triggered the AppleID issue, it may have been "Block all incoming", or "stealth mode", or…? It would seem that following significant changes or upgrades to the OS ones computer needs to re-establish an authenticated handshake with iCloud, by a different than everyday method is normally used to sync documents and data, and that a firewall blocks this initial handshake.
This may explain why some folks who have an effective router based firewall also have problems setting up iPads and iPhones.
Goodluck.
One could have reasonably have expected that Apple (the slackers) would have long since fixed this problem, or at least notified a workaround in the posted iCloud trouble shooting knowledgebase. This OS centred problem differs, from the earlier ICloud Authentication problem that was server based and affected users with very old AppleIDs that were flagged "Apple Retail Product Professional" which was caused by iCloud's database not recognising the Flag.