I've seen tons of jeans on Alaska cruises and at dinner on non formal nights. Jeans are not an issue on Princess. Just keep in mind that if you wear them for wet shore excursions, they're going to take a very long time to dry and will be heavy. Lighter waterproof material might be better.
Everyone has an opinion on jeans at dinner, but the cruise line is absolutely fine with them on non-formal night. Enjoy Alaska, it's beautiful