The registry key mentioned on the top of the exception (HKLM\Software\ABB\AFW\SystemModules\DataSubscriptionManager\1.0-0\private) should be open and readable by all users of 800xA. On 64-bit OS the actual registry path is slightly different (HKLM\Software\WOW6432Node\ABB\...).
Have you applied any custom hardening policies or GPOs preventing registry access for non-admin users?
The installer and service account have administrative privileges which is expected, but regular users should not need admin rights.
If you have any client where this problem is not showing up you could compare the registry protection settings in an attempt to spot why registry access is denied.