Mojave: disable or control the "[SOME_APP_NAME] wants access to control [ANOTHER_APP_NAME (often Finder)] ..."?
Add the app to "Full Disk Access"

In Mojave, under Security &amp; Privacy, there is a new tab called "Full Disk Access".

Adding my personal Applescript apps to this list (in addition to the existing Accessibility list) has made the prompts disappear.



Update 9/26: Upon a couple days of further use, this seems to work sometimes, but not consistently.