Unless your port of departure is involved in a severe storm or hurricane, you'll be fine. They will most certainly change the itinerary. The ship's move faster than the storms, and they are VERY aware of the weather systems and forecasts.
You may not get the itinerary you chose, but go with the flow, and enjoy the cruise you get. They will be keeping your safety in mind... and of course that of their 400 MILLION dollar ships <G>
Neither Carnival nor any other cruiseline is in business to "hose" people, as you put it, and cancel their cruises at the last minute unless circumstances make such action unavoidable. As Kuki mentioned, you might find your itinerary changed or you may miss a port or two because of weather conditions (believe me you wouldn't want to maintain the same itinerary if it puts you directly in line with a tropical storm). There are no guarantees especially when weather is concerned, so you have to be flexible and be prepared to adapt to changing conditions. Tropical storms and hurricanes are powerful storms and their effects reach out hundreds of miles beyond their center. Their paths can also be difficult to predict. Cruise lines don't enjoy changing their schedules or itineraries anymore than you do, so give them the benefit of the doubt when such occasions arise.
Sundy, there was a good example of "cruise itinerary changes" just last week on the Pride. The water was too rough to tender to Half Moon Cay, so they sailed to San Juan. The next port of St. Thomas was OK, St. Martin had to be cancelled due to a "bomb scare on land". Three cruise ships were turned away! Captains of these multi-million dollar vessels will not risk the lives of their passengers or the sake of their ships
under any circumstances if at all possible. Passengers must read the very fine print and be aware that these changes can and do occur. Let's hope the end of June has great weather for you, too. I will be in the Pocono Mountains that week with my 3 grandkids. Pray for sunshine or they will be brought back to New England! This is my first land vacation in 5 years.
The ships will do everything they can to avoid a tropical storm (and they can do a lot). Nothing could be worse for a cruise line to not only loose their $500,000,000 plus investment in the ship, but to have to deal with the bad publicity too.
Modern cruise ships have sophisticated weather monitoring equipment on board, in additon to links to land based weather stations. Ships can easily change their itenerary to avoid bad weather. A common change is for a cruise that is scheduled to take an Eastern Caribbean route (a common one is San Juan, St. Thomas and Ste. Marteen) and change to a Western Caribbean itenerary (for example, Jamaica, Grand Cayman, Cozumel).
The only scenerio where a cruise would be cancelled is if the home port was threatened by a storm. Under that scenerio, the cruise line would either refund the entire cruise fare, or reschedule you for a later cruise (at whatever time you choose), and often offer a substantial discount on a future cruise (50% off or more is not unheard of).
You are cruising in late June. Most tropical storms form in the Gulf of Mexico that time of year, and move onshore between Corpus Christi, TX and Panama City, FL (although exceptions do happen). I wouldn't worry about the weather. You will probabilly have a rougher flight than a cruise. I would also be as flexable with my travel plans as well.
In mordern times it was only last year that a couple of cruises were ever cancelled due to weather and those were Bahama and Bermuda cruises. All other times the ships have been able to just change ports and move around the storm.