My ex had her tires rotated at Sears a few years ago. She had directional tires and they X'd them. They made a ton of noise, and I investigated after the first time I got in the car with her and noticed how loud it was. Brought the car into my work and swapped them back, road noise was greatly reduced.
I imagine that you would have similiar results if they were backwards. Suppose it is probably pretty rough on the tires, just judging by the racket/vibrations they made.
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