Although I'm not a big fan of
DCL generally (I think they are hugely overpriced), Hurricane Season is not the problem for cruises that it is for land resorts. We have a hurricane season for precisely one-half of the year - every single year - so the cruise lines are well-accustomed to dealing with whatever bad weather the season brings.
The only real issue with cruises occurs if a storm threatens your cruise port at some point. Ports tend to remain stationary, so they are vulnerable to hurricanes. If it occurs just prior to your scheduled cruise, they may not be able to get the ship
in on time for you to sail. If it hits when you are supposed to land, they'll probably just re-route you to Miami and transport you whereever you need to go.
The good thing about cruise ships and hurricanes is that cruise ships move. At sea, they simply go around storms. A cruise ship is much faster than a hurricane and they don't go within hundreds of miles of bad weather. They usually just scoot around to the back side of the storm and have perfect weather. In some circumstances, that could mean you would not hit some port-of-call you were looking forward to, but then again you might get a huge bonus by going to a different port.
I can think of several reasons not to take a member cruise, but hurricane season is not one of them.