I've a problem:
I've changed my apple ID a week ago in ios 6. Everything was working fine until I've updated to ios 7 today. In ios 7 I've to re-enter my iCloud id password. That's not a problem but the password isn't accepted. This is because the iCloud ID is still configured to use my old apple ID! It's greyed out, so I can not change it. The solutions that I've found all telling to delete the iCloud ID first and then to connect it again with the new credentials...., but in Ios 7 there is a new security feature: To delete the iCloud ID you've to first logon to disable find my iPhone! I can't logon beause of the wrong id :-( the chicken and the egg....
Please apple help!
I had the same problem as I had changed my email for my apple id but the icloud still had my old email.
Only way round it for me was to login to my apple account and change my email back to my old email which I then had to verfiy.
Then my password worked when trying to disable find my phone.
I then deleted my icloud account ( Under settings - Icloud )
Then changed my email back to my new email account - verfiy again - then the login worked.
A lot of hassel but this seemed to work for me
Login for Mange apple id https://appleid.apple.com/cgi-bin/WebObjects/MyAppleId.woa/