Hi! I am a veteran cruiser on RCCL. You do not need to wear a tux on formal nights. The majority of men wear a suit and a tie. Very few actually wear tuxedos. Some men even just wear nice pants, dress shirt and a tie. I too have even seen people wearing polo shirts and Khakis but, they are far fewer than men in suits. I usually wear a cocktail dress.
Hope that helps!