Transfering an app's data to a new Apple ID.

Hello,

Recently I've switched my iPhone to a new Apple ID. I've transferred all my iCloud data successfully;

however, I ran into a problem when trying to update apps on my iPhone. The app store won’t let me do it, and demands I log in into my old Apple ID.

I’ve looked online for solutions to this problem, yet it seems like the apps I downloaded with the old ID are tied to it, and unable to be unhooked. Meaning, I have to reinstall the apps to be able to fully use them again. This is a problem, as one of the apps on my iPhone has a lot of important data to me, all stored locally on my iPhone. I can’t afford to loose that data.

Is it possible at all to move/transfer apps from an old Apple ID (the app didn’t use any of Apple’s services) to a new one? Or failing that, is it possible to export and manually backup an app’s data so that I can put it back later after reinstalling it?

Thank You for the help.