How do I prevent content refresh on iOS 13?
There's no global way to do this because it's under control of the app developer.

Each developer can decide how they want to refresh the data and the view you're seeing.  In these instances, CNN &amp; Instagram developers decided to keep that this was the behaviour they wanted to give you.

Some developers, for example, Tapbots (maker of Tweetbot), provide an option in the app Settings to allow their users to change this refresh experience.

Because there no global setting to control this, you would need to contact the developers of those applications and ask them to include this feature.