Every time you board the ship and every time you enter a food area, you will be expected to use Purell hand sanitizer. Staff members will be holding dispensers and you WILL be stopped and questioned if you don't use it. I totally understand their reasoning, but it can be problematic if you're allergic to the stuff like I am. Explaining the situation and promising that you JUST washed your hands might get you by, but they won't be happy with you.
Thankfully, I'd brought along a small bottle of alcohol-free sanitizer spray, thinking it might be useful in port. I ended up keeping it in my pocket and letting them see me using it whenever we went to eat. I highly recommend you do the same if you can't (or don't want to) use Purell.
That said, we enjoyed our cruise very much.