I don't have enough experience to speak about CC in Germany, but I don't see why a Rewe or ... boh, Aldi, Mcdonalds, etc should prevent that. I am a bit surprised, to be honest.
The bigger mystery is why stores in some other countries are happy to have a payment method chosen by the customer eat into their profit.
But actually a lot don't, and when you try to pay, even contactless, with a non-Girocard, it won't work.
Visa and Mastercard don't magically let you on their network because you have a card machine.