This would likely require a massive rewrite. This all goes well beyond just ERPNext. Mariadb’s date field is hardwired to the Gregorian calendar, and using another calendar as default would require some fairly low-level code design.
On the ERPNext side, you could definitely do what you’re talking about, but you’d have to handle each issue like birthdays individually.
The best approach here wouldn’t involve modifying core files. Just include a new JS file in your custom app that extends the base class. If you want to see where the class is defined, just run a search for the classname “ControlDate” in github.