Let’s say I become a citizen of a country that doesn’t allow dual citizenship. During naturalization, new country B tells me I have to renounce citizenship from old country A.
Does that have any effects back in country A? How would country A know? Would country A even care if they found out?
Hmmmm what? The USA absolutely allows dual citizenship.
https://travel.state.gov/content/travel/en/legal/travel-legal-considerations/Relinquishing-US-Nationality/Dual-Nationality.html
Yes, I mentioned that the US doesn’t care about dual citizenship. But the naturalization oath might suggest otherwise:
https://www.uscis.gov/citizenship/learn-about-citizenship/the-naturalization-interview-and-test/naturalization-oath-of-allegiance-to-the-united-states-of-america
There’s an apparent discrepancy between the oath and the US official stance on dual citizenship (per the links you posted).