Today I have activated Cisco Finesse on UCCX and I am also facing the same problem. CUCM local users are able to login successfully but not the LDAP users. We are using version UCCX 10.5.1.10000-24.
The problem is solved by referring to this bug:
After removing the all the admin user rights in both CM and UCCX, need to wait for a few tens of minutes before it works.
But still, don't understand why there are difference between LDAP synchronized account with LDAP password authentication and local user End user account.
Our Local user account has the admin right but still can login finesse desktop.