On the contrary, I think that the most serious potential problem for the internationally exposed sectors is not short-term exchange rate variability, but medium-term misalignment in the exchange rate. Allowing market forces to move the exchange rate makes such an outcome much less likely.
Better monetary control afforded by the flexible exchange rate, on the other hand, has been an unalloyed benefit to all sectors of the economy, traded and non-traded. Lest this sound as though we never have a care in the world about the exchange rate moving, however, it is important to add one caveat to this story.