Is it safe to delete all color profiles in /System/Library/Displays ?
No, the system uses at least some of them to control the color of items it displays in the interface. sRGB is there for Safari and other web browsers. Any image that has no profile is then displayed with sRGB as an assigned profile since that's the most commonly embedded profile for web images.
Your issue may be a corrupt .plist (preference) file. In your user account, go to the ~/Library/Preferences/ folder and move this file to the desktop:
Log out and log back into your account. Choose your display profile and see if it sticks. It should. This preference file holds a variety of settings, so you'll have to go through the System Preferences and see what else you need to change back to your preferred settings.
Then it's the other file. Trouble is, I can't find my note on it. It has to do exactly with what you're seeing. You choose a monitor profile, but it won't stay there. I'll keep looking.
In the meantime, check to see that it is account related. Create a test user account and try it there. If that monitor profile choice sticks, then the issue is definitely somewhere in your account.
Ha! Found it.
If the "Show profiles for this display only" button becomes stuck permanently on, remove the following file from your user account in the ~/Library/Preferences/ByHost/ folder.
The numbers following "com.apple.preference.displays." will likely be different than what you see here. But that's the file to remove.
The text I saved (as you see) had to do with a button in the settings getting stuck, but may also be the answer to the profile choice not sticking.
Thanks for your efforts and hints. Prior to your reply I found this help: http://reviews.cnet.com/8301-13727_7-57540493-263/how-to-make-colorsync-profiles -stick-in-os-x/
And it worked.
open $(getconf DARWIN_USER_CACHE_DIR)
Show your user id (UID) with: id username.
Note: don't change color profile directly, log out and in first.
So I can't confirm if deleting
When I unplugged my MBP from the Cinema display and all the problems came back, I tried to create a test user account for verifying. And it appears as if the test account works fine. And one other thing, the log in screen always looks good.
Still not really solved. OS X has been acting all weird lately.