Keep the Select by Color tool active and have it redo the selection with the previously chosen color on active layer changes
Operating System: Any
Select by color code
The relative with Select by color, Select by color code selecting by HTML notation will select automatically while it's activated and change the selection if the layer will be changed and uneditable until deactivate, or if it was deactivated it just will do selection with enter key.
Mostly a stacked animated green screen will be a huge issue because for every layer to change selection you had to click every layer once at a time, by Select by color code it will not be a huge problem because it will change selection if the layer changes and if it's activated.