Just got back from 10-day land tour on RCI Vision of the Seas (July 22-Aug 1 northbound). Except for 2 formal nights (I have a tux and took it), on-board dress is comfortable and casual. I wore jeans and casual shirt (not t-shirt) all the time, even to dinner, as did everyone else. My wife wore slacks and casual blouse except formal night. The land portion is even more casual and comfortable. Take layers as the temperature can change quite a bit in a day and take rain gear of some sort, even if it is just a slip-over poncho.
One morning in Fairbanks it was 42 and generally speaking it was cloudy and misty along the coast as well as inland. We took a 3-hour whale watching excursion in Juneau and it rained the entire time, was soaked to the skin, and nobody complained since we saw so many whales. One Orca pod even bumped our whale-watching boat. It was clear in Ketchikan and that is very unusual since they get several hundred inches of rain a year.
Bottom line, dress to be comfortable and not to impress anybody because you won't. As they said on the land tour, nobody in Alaska cares about the way you look.