No, it’s highly dependent on the countries involved. When you apply for the second citizenship, that country knows about your first citizenship. They can decide to force you to choose one. And the first country may or may not allow you to give up that citizenship. As an example, you can read about dual citizenship in Europe here: https://m.dw.com/cda/en/dual-citizenship-in-europe-which-rul...
You will see that the rules differ by country.