Earlier quoted context omitted.
I don't know where you're at but I have never seen this treated as that big of a deal in my 8 years of living in Austria & 7 in Germany unless you're talking to the prime minister (and especially not if you're obviously not a native speaker). Maybe more comparable to addressing someone by their first name instead of Mr./Ms./Mrs. .
Du/Sie and first name/last name are almost without exception divided along the same lines in German. Sie plus first name is how a person with extreme status expectations would address their butler, and just as old-fashioned. "I'm sorry you can never be my peer but I respect you anyways". Last name and Du would be using the last name as a nickname in a decidedly first name situation. Think "bro" but timeless.
I can vouch for the Kassiererinnen-Du being used. My mom runs the butcher in a supermarket. She and and many of her coworkers share a lot about themselves, but they still address each as other as Frau Schmidt and Herr Schulze.