Can iOS be configured so apps do not create screenshots when the app suspends? I notice in iOS, often times when I open an app, such as YouTube, the first thing that it shows is a screenshot of that app from one of the more recent things I was doing with the app. 

When I multitask back to the app, the OS loads these images before the app is fully running and able to process input.

But it strikes me as useless, since the buttons on the app don't even function at that stage, and it even does this for apps that don't fully restore state so you see it go back to a main screen after showing you what you were doing in the app before. It's also a security concern because I could be writing in a password-protected note or something and it shows up briefly when opening the app, or an old YouTube video screenshot could show up when I'm opening the app.

How can this "featured" be turned off in iOS.
There's no global switch in iOS 9 or earlier. The app developers can decide, what the app show during loading. 

If you see security issues or just feel that the experience using this feature is poor, the only remedy today is to contact the developer. Many professional apps like 1Password and Apple notes are coded to not disclose secure information in a temporary app image. 

Another option would to be to send feedback to Apple or a bug report detailing any lapses or explaining how this should be an optional control. Apple could change this in future OS if a case were made well enough or by enough people.