I think it depends on the embarkation port and quantity when it comes to soft drinks. I also saw people boarding in Cozumel carrying sodas and bottled water they'd bought ashore. Again it wasn't cases but just one or two bottles.
On the Allure last month we had a some small bottles of Coke in our carry-ons. We really didn't think of the policy and brought the soda we had in our hotel room. Nobody said a word about it and we had it on the ship. In fact, it really didn't occur to me until I read this thread that we had unintentionally violated the policy.
While I can understand the alcohol policy I do find their official stance on soda and water to be needlessly cheap and driven solely by a desire to increase sales of their bottled water, juice, and soda packages.