Koshka, i have sailed on Princess many, many times and i will tell you that i have never seen anyone in the main dining rooms on formal nights in jeans or shorts. 100% of the men and boys either had on dark suits, tuxedos or sports jackets dress slacks, dress shirts , few sported banded collars that don't require ties, most had on ties.
All of the women were either in gowns,long dresses, dressy long skirts with dressy or sparkly tops, dressy cocktail dresses or dressy pants with dressy/sparkly tops.
This should be a NON-ISSUE because ALL of the cruise lines offer casual dining ALTERNATIVES to those who do not want to dress up on formal nights, if you plan on dining in the MAIN DINING rooms on formal nights, you should dress accordingly. Its just common courtesy towards your fellow passengers who enjoy getting dressed up and take the time and make the efforrt. IF you don't want to get dress-up on formal nights, that is FINE, just choose to dine in one of the CASUAL dining restaurants those nights. I will get off my soapbox now.