SSDT - Deprecated table trigger preventing publish
There is a setting on the "drop" tab of the advanced publish settings called "Drop DML Triggers not in source."  This is checked by default, and thus triggers should be dropped by the publish process.  This is true even if "drop object in target but not in source" is unchecked.

It sounds like this has been unchecked in your publish process.  You can confirm that by looking for this element in your publish XML file (if that's how you're publishing):

&lt;DropDmlTriggersNotInSource&gt;False&lt;/DropDmlTriggersNotInSource&gt;


Removing that element, or setting it to true, should resolve your issue without setting the undesirable "drop object in target but not in source" or having to use a pre-model script.



Regarding the inciting issue:


  There is a table trigger that was removed in the past that is blocking SSDT publish preview (due to a dependency)...


If the setting I mentioned above doesn't resolve the problem, it would be helpful if you could provide a repro steps for this scenario.