How do I prevent icons from being added to the dock?
How can I prevent this icon from showing up in, and getting pinned to the dock in macOS 10.14?


You can't.  

Your Mac is under MDM policies and thusly you can't override what those policies are.

The setting "Keep in dock" has no effect on a separate process that checks to see if an item is in a dock and manually putting it back.  Think of it as you, the user, removing an item, then coming back and manually putting the icon back to the dock; that setting would have no effect there either.


  There is an option to disable the dock icon in the utility config, but
  its effects are org-wide and they won't disable it.


This statement confirms this.  The MDM software/process has the ability to insert the dock icon per its configuration, but, as you stated, your IT organization doesn't want to disable it.  The "trick" that you mentioned was probably addressed in a bug fix.