Can't remove LDAP account from Internet Accounts
UPD: I've updated to Mojave and was able to delete these accounts.

I have the same problem on High Sierra (starting from 10.13.4, currently up to 10.13.6).

I tried to reset my iCloud keychain. It worked, until my iPhone (6S+, iOS 12.1.4) got connected to Wi-Fi and pushed data with those accounts back.

I checked this again, by disabling iCloud keychain on iPhone (Settings > Passwords &amp; Accounts > iCloud > Keychain > Off), then resetting iCloud keychain on Mac, and then enabling back iCloud keychain on iPhone.

Seems the solution is to reset the iPhone (and other iOS devices, supposedly) and then reset iCloud keychain via Mac.
But I'm not ready to go so far to test this theory, unfortunately.

Below is how to reset iCloud keychain from previous version of this answer.

You should probably backup your login and iCloud keychains, to avoid losing passwords and having to re-enter them after reset.

Login keychain stored in login.keychain-db file which is located in ~/Library/Keychains/ (Finder > Go > Go To Folder (cmd + shift + g). 

You can copy it somewhere safe and then add it back (Keychain Access > File > Add Keychain) 

Unfortunately, it's not possible to do the same with iCloud keychain.
There is other solution.

To reset keychains:


Open System Preferences > Internet Accounts > iCloud
Uncheck Keychain in the list
Open Keychain Access > Preferences (cmd + ,) 
Press Reset My Default Keychains button


Now go back to System Preferences > Internet Accounts > iCloud


Check Keychain back
Enter your iCloud password
Click Use Code, then choose Forgot Code when you're asked to enter your iCloud Security Code
Click Reset iCloud Keychain to confirm
Follow the onscreen steps to create a new iCloud Security Code (should be optional)


See https://support.apple.com/en-us/ht202755