My parents prefer I call them by their real names, is that weird?

I personally would also want my children (if I ever have any) to call me by my first name. I don't perceive it as disrespectful to call their parents by their first names.

Our parents gave us first name for a reason, be it because it is tradition or because it is the law. Why use substitutes?

Things evolve with time and so do names. You barely hear a child nowadays being called Aglaea or Amadeus. You are more likely going to find a girl named Soutwest or a boy Norheast.