Poking fun at regional accents is one thing (and common in Germany too though I'm no good at doing impressions of other regional accents, my wife is though), but ethnic accents of immigrant minorities is another matter. At the time, I wasn't ridiculing a Miami accent but Rudy's then (it was his Whitesnake era, judging from more recent interviews he's lost most of it) inability to speak "proper English" after decades of being an American (but probably in an environment where most people around him continued to speak Spanish), he sounded like a Mexican bandido with gun belts across his chest in a 50ies black & white cowboy film. In hindsight, my pronunciation arrogance left a sour taste with me (long before 'political correctness' became a catchphrase) though I am generally not perceived as being all too touchy - or hesitant - as (my own) low pc remarks go.
Whenever I hear the brilliant Tom Lehrer say a German word or phrase, it becomes evident to me that he must have grown up hearing and/or speaking fluent German. Some second generation immigrant story behind that. His parents, Moses and Anna, secular Jews, came to America before darkness engulfed Germany and most of Europe.