I think you will find that many of the ports in more impoverished areas within the Caribbean that are called on by cruise lines tend to be anti-gay, simply because of the lack of education their culture has received over the decades.
Does this mean that random people you run into along the streets will glare at you, or will you be turned away from shops, etc.? Highly doubtful, but not impossible; I personally have avoided cruising to Grand Cayman in particular because it has a pretty nasty reputation on the gay issue.
Plenty of other islands, however, such as Bermuda and Key West, have a more open stance on the issue and welcome gays to their home.
Gary Kulash
www.badelephant.com