Here's a brief synopsis from IMDB:
And a snippet of dialogue that tells you what the characters are thinking:
Lucy: HAVE dinner?! He wants us to BE dinner!
The second and bigger problem is that the characters are one speedboat ride away from Miami Beach. What's the normal range of a speedboat on the open seas--10 or 20 miles? I'm pretty sure there are no islands, deserted or otherwise, that close to Miami.
Not unless they're chock full of resort hotels, that is. The idea that you could have a "desert island" within hailing distance of Miami Beach is ridiculous. Every island for miles would be owned, occupied, and developed.
That this ridiculous notion of a desert island could be inhabited by man-eating Indians is even more ridiculous. There are no uncontacted tribes in the Caribbean. No reservations where life continues unchanged. Caribbean Indians have been (forcibly) assimilated into European-style living for 500 years. The last "primitive savage" probably died a few decades after the Spanish started colonizing the islands.
Yet Lucy and Ethel are so ignorant they believe a wild Indian will eat them?! Would they expect an English doctor to bleed them if they were sick? A Japanese official to skewer them with a sword if they broke the law? No, but they have no problem envisioning Indians as throwbacks to another century.
It's one thing to be wary or fearful of a stranger, but I presume they've heard of Sitting Bull and Geronimo, at least. You'd have to be beyond ignorant to think cannibals still exist in America or its immediate vicinity. Yet Lucy and Ethel--or the writers who put the words in their mouths--believed this.
The fact that it's a white man in a costume is irrelevant. Other than as an example of the prevailing redface of the era. Lucy and Ethel believed he was real--believed cannibal Indians were roaming just off the coast of Miami.
What it tells us
Another episode I saw had a black man as a train porter. That's also stereotypical, but it's infinitely better than an Indian as a cannibal. The equivalent would be an half-naked African in a grass skirt--but people knew enough in 1956 not to do that. But they didn't know or care enough about Indians to avoid this blatant racism.
This episode is a classic example of how stereotyping works. Most of Lucy's viewers probably didn't think much about the Caribbean. They may not have paid much attention to this episode or its depiction of an Indian. But it undoubtedly influenced their perceptions anyway.
If you asked them about Caribbean Indians after the show, I bet they'd spout the usual stereotypes. Even if they discounted the show, it reinforced what they already believed. Indians were killers and cannibals--and if any are still around, they're still savages.
For more on cannibal Indians, see Cannibal Indians in Green Inferno and Cannibal Indians in My Ghost Story.