How to turn off "Add file to git" in Intellij?

I'm not sure if this is exactly what you're looking for but let me try.

Settings marked with a console icon are only applied to the current project(Read this article). So when you create a new project (or open a new project), it defaults to "Ask". However, you can change that in File -> New Projects Setup -> Settings for New Projects... which will open the same settings window for you but these settings will be applied by default if you create/open new projects in Intellij. Setting this to "Do not add" should be enough to never get the "Add file to git" pop-up window again.