*Cruise passengers who are disembarking at Bridgetown, the island's capital city -- whether staying on the island for a post-cruise visit or heading straight for the Grantley Adams International Airport -- must have that passport. This particularly affects U.K. and European travelers, whose ships more commonly than U.S.-based vessels, use Barbados as a winter-Caribbean-season homeport.
*All other passengers -- those for whom their cruise begins and ends somewhere other than Barbados and for whom the island is just one in a handful of stops on their itinerary -- are considered "in-transit." As such, these folks are not subject to immigration control and a passport is not required. They will be allowed ashore as long as they have their ship's card.