I am having the same problem. It's infuriating. I just changed my primary email connected to my appleid and all is well when I sign in on my Macbook, but my iphone just isn't having it. It's been a while since you've posted this. Has it worked out since then? Some people were telling me it just needs a few hours because I newly verified my primary email address. Hopefully it's all worked out for you, then I will know there is hope for me.
infuriating for sure.
I ended up dealing with the problem by deleting my appleid on my phone and then creating it again. After that, it worked fine. But I was really annoyed that the problem came up in the first place, and especially after hearing so many other people had the same problem. It seemed like a pretty obvious bug in their upgrade, and yet they seemed totally indifferent to it. I have never seen any official acknowledgement of this problem, yet the problem looks really widespread.
I hope you get yourself back on track, with this or some other solution.
I deleted it in settings/mail,contacts.../icloud account
at the bottom of that screen is a 'delete account' button.
once I got icloud working well on my devices, I discovered another problem: photostream takes the last 30 days of photos from your library and sends them around to your devices. That's great, but it works by date only which means it takes images out of the trash and out of my real folders. So photostream is clogged with images I trashed, and you can't (as far as I can tell) tell it not to take those. It's mind-boggling annoying.
Anyway, I wish you happy times with icloud.
Overall, though, I do like it for its good features. But it does have a surprising number of annoying ones.
Oh, THANK YOU! I am shouting with joy! Have been dealing with this problem for a couple of weeks now and you solved the problem with such a simple task. This is my first "smart" phone (a hand-me-down from my son) and it has proven to be a whole lot smarter than I am! At least now I know where to look for answers.