Although Princess's policy is that they do not allow jeans in the dr on casual nights (and many people will frown upon them) I've been wearing them for years on casual evenings. Even on formal nights I change into jeans before the shows. I suppose the more relaxed atmosphere is due to the varied dining times that weren't a choice years ago. I imagine that if you showed up in raggedy torn jeans at the dr door something might be said but as long as they're in decent condition you'll be allowed to dine.
On one of our last Princess cruises (Caribbean P) they posted that no shorts were to be worn in the dr for breakfast or lunch. They also printed in the patter that no short sleeve shirts were permitted for dinner on formal evenings. Again these requests were not enforced. I always dine with my jacket off & do not own any long sleeve shirts or ties.