No, cruise ships are not allowed to dump solid waste, including trash, into the ocean. Instead, they store the waste on board and bring it ashore to be properly disposed of.
Do Cruise Ships Dump Their Waste In The Ocean
Modern Cruise Ships Only Dump Treated Waste In Oceans. Cruise ships do dump sewage into ocean waters, but with modern ships, it will only be after that sewage has gone through extensive treatment to remove anything harmful. Certain waste waters are released.