As someone else said, you'd be surprised what people get away with. People do wear jeans and shorts in the dining room, including formal nights, although they are in a minority. Kids (especially young kids) definitely wear shorts more often. Most everyone makes an effort to ensure the shorts/jeans are a nicer quality and can look dressed up with a polo. I've been on 9 cruises with Royal - There have been people at my table almost every cruise that wore jeans almost every night. One guy wore jeans and a tuxedo tshirt on formal night. Haha!
DH doesn't take a suit usually anymore. For 7-day cruises he'll bring one or two pairs of khakis, a pair of nice pants, a couple button up shirts, polo shirts, and a tie. A suit takes up too much space in the suitcase. I bring one pair of khakis, a black skirt, and tops for dinner. We also change back into our shorts and tshirts right after dinner, that way we can wear our dinner clothes multiple times.