I have this problem too. What the flip Apple have you done now!!
Q: Is there any way to change the Apple ID you use inside the app, to NOT be your iCloud one??
Like millions of other users, I use separate iCloud and Store Apple ID's (thanks to legacy that Apple refuse to even acknowledge, never mind address!)
This now completely screws-up being able to use the sodding thing on any of my iOS devices! No really Apple, this is the stupidest forced decision yet, you've really outdone yourselves with how much you can infuriate customers, yet further?!?