Our GTI (and previously Golf TDI) sets of winter wheels required centering rings... They were MSW going on VW hubs. I ended up leaving the rings on the wheels with no ill effect, just make sure they don't get lost. They seem flimsy but they are not weight-bearing, never caused any wobbles.
Wheel/tire minutiae... The worst was the S4 where I went with BBS SR for winter. They required centering rings AND different bolts (conical vs. spherical). And they needed locks as I occasionally parked outside and they were more than decent for winter wheels. And that lock set needed to be different from the summer lock set. So two sets of wheels/tires, centering rings, two sets of lug bolts, two sets of wheel locks, none of them interchangeable.
Fun times at the tire shop during swapping... I go to a shop where I can 100% supervise/micromanage the process.