How can I reference a different public static variable in different instances of a prefab?

So here’s the rundown:
I have a script attached to a star prefab that causes it to rise out of the ground when the player solves a puzzle. The star is triggered to move by a public static bool that is set in a different script when the puzzle is solved. I use the star several times in the scene, each for a different puzzle. I want each star to do the same thing, but they are all triggered to move by a different public static bool. I know that I could solve this by creating a separate script for each star, but then I would end up with a bunch of repetitive, almost identical scripts.

Is there a way I can make each star reference a different public static bool variable without creating a unique script for each one? Any suggestions would be very helpful.

No. There can be only one object per static field. Marking a field “static” means there will ever only be one of it.
The only way is to create a script per star, although in your case it sounds like you can use the same star object for all of the puzzles (unless multiple stars need to appear on screen at the same time).