At least in Haiti, no one really listened to American missionaries until America occupied the country in the early 1900s, displaced local elites, and essentially turned the place into a neo-colony. The circumstances are completely different in other Caribbean islands, but the point is that the spread of homophobia in Haiti is pretty strongly tied to increasing American dominance over the Haitian economy and politics which translated to increased cultural influence. America has never occupied Denmark, attempted to monopolize the Danish economy, and replaced rich Danish people with rich black Americans.
Now there were indigenous Christian Haitians who also would have been homophobic; namely Francophone Catholics. However the spread of homophobia cannot be attributed to their influence because historically speaking they have never exceeded 5% of the population and the other 95% has been loathe to adopt anything from Francophone Haitians, to the point that in Kreyol li pale franse, lit. "he speaks French" is actually an insult. We don't really see serious penetration of Christianity into Creolophone and rural Haiti before the American occupation IMO, before that the area was pretty much 100% Voduisaint. In addition, the indigenous Francophone Catholics are actually pretty socially liberal on areas such as homosexuality and abortion.