Recently I've heard "We are all living in America" in the text of America from Rammstein. Does this phrase make any sense or is there "are" just to fit in the rhytm?
It just means "We all live in America." but the Continuous aspect emphasizes the activity of living (each day we live, work, eat, etc.) rather than the state (America is where we live).
Based on the lyrics, the meaning seems to be saying that all the world is participating in America's culture, maybe a cynical way of admitting how much America influences the rest of the world.
It's also possible that the difference in grammar is due to Rammstein's native tongue being German, as German doesn't use the Continuous "ing" form, but I think that it's just as likely that they understand the difference and are using it as I indicated in my first paragraph. We are living in America, day by day, participating in American things, regardless of where we live geographically.