I wouldnt wear jeans in the dining room on any night, but if someone wants to it doesnt bother me. I like getting dressed for dinner both on a cruise and at home. It makes it feel like more of an event for me. I do wonder why someone would want to wear jeans on a tropical cruise though? Khakis are far more comfortable. On formal nights I would say it is a must to dress nicely and have your children do so otherwise choose another dining option.
On the other hand people who get all worked up over people who dress casually on non formal nights or other parts of the ship really must have small lives. Its a vacation relax. If you are getting worked up about something so small perhaps you should consider medication instead of a cruise. Theres so much to do on a ship and if you have time to worry about other peoples dress you arent getting the most out of your cruise.