We usually eat at Chops at least once during a cruise, and have never seen anyone there in shorts. Occasionally, I will wear a jacket and tie at Chops, but usually it's just dress pants and a golf shirt.
Shorts are OK in the main dining room for breakfast and lunch, but definitely NOT at dinner. Also, no swim suits in the MDR.
We are doing back-to-back-to back cruises on Navigator next month, and have decided to skip the MDR and eat in the Windjammer every night. We'll also go to Portofino at least once on each of the three cruises. This is a "radical" move for us, since we normally do the MDR for dinner. We just decided to do something different this time.