I had a similar problem. Every time I opened a CC App, I was asked to sign in. I followed instructions on several forums, but nothing worked.
Yesterday I got in touch with Adobe Help and together we spent over two hours trying to resolve the problem. I have to say Khongyairong (the guy I was dealing with) was very helpful but we ran out of time as I had to go out.
Today, I decided to remove every single trace of Adobe from my Mac. I followed these steps and all now works as it should! 
Please note the order – uninstall apps first, then run cleaner, then manually remove any left over files.
Warning: You will delete all Adobe files from your computer. If you are using any Adobe products other than Creative Cloud please make sure you check every file before deleting it – if it's not related to CC don't delete it! You might want to make a snapshot of your system that you can restore to before doing this. If there is more than 1 user on the Mac make sure they don't have Adobe products that could be effected by the following process.
- Use the Uninstallers for each App you have (uninstallers can be found in Applications/Adobe *App Name*/Uninstall Adobe *App Name*
- Check Applications/Utilities for any other Adobe Uninstallers and run them
- Use Creative Cloud Cleaner to remove everything else (I was given the download from Khongyairong so don't have the link)
- Select 'All' from the dropdown menu, top-right.
- Click 'Clean All'
- At this point I restarted my Mac but it may not be necessary.
- Go to /Library/Application Support and delete the entire Adobe folder (I also deleted the Macromedia folder too, but I think this is just for Flash Player)
- Go to /Library/Caches and delete all folders and files with 'Adobe' in the name
- Go to (User) ~/LibraryApplication Support and delete the entire Adobe folder
- Go to /Users/Shared/Library/Application Support and delete the entire Adobe folder (if you have more than one user set up make sure they are not using Adobe products that will not function correctly if you delete this folder)
- At this point I searched my entire computer for any other files or folders with Adobe in the name and deleted them
- There was also a Photoshop folder in one of the Librarys (can't remember which but check in both) I deleted that too
- I emptied the trash and restarted here and would recommend the same
At this point I could have started installing the software again, but I took some extra steps which involved 3rd party software. I use Onyx which is a very good tool to clean up OS X system. You can use this or something similar to do the following:
- Reset home folder permissions and ACLs
- Clear system and user caches
During the Onyx processes I was promted to restart my Mac a couple of times. Once all that was completed my Mac was booting up a fraction quicker than before (which was a nice bonus).
Fresh installs
I then went to creative.adobe.com, signed in and downladed Creative Cloud Desktop App – nothing else.
I installed CC desktop, signed in and initially downloaded 1 app (in my case Photoshop), opened it and waited... no window requesting sign in!!!!

I double checked, by quiting and reopening Photoshop – all seemed good!
I was then able to install other CC Apps (one by one just be sure) from the Creative Cloud App and every one of them works withut being promted to sign in!
Hope this works for you, I've seen this issue a lot and was very happy to have a solution to share it with others!