It could be the gentle weather, or perhaps the soothing breezes that float perpetually off the sea. Maybe it is the insouciant beauty of palm trees rustling on the edge of white-sand beaches.

Whatever the cause, and maybe it has nothing to do with the setting they live in, the people of the eastern Caribbean enjoy an unusual tolerance for one another's oddities. As a result, eccentricities flourish in these little islands as easily as bananas and ganja. Few seem to mind or even pay much attention.

A young political activist in Guadeloupe, for example, ends a telephone call on that French island north of here by intoning in all apparent seriousness: "Au revoir. Vive la France. Vive le roi."

The middle-aged woman sitting next to him does not react, seemingly able to accept that a young man on a Caribbean island in 1985 should be wishing long life to a king whose rule far-distant France overthrew for the last time more than a century ago.

HERE IN GRENADA, remnants of Maurice Bishop's New Jewel Movement also seem to be looking back in history. They have organized a new party, with little apparent following but with a lively weekly newspaper. Despite the seriousness of their cause, the leftover revolutionaries have baptized their paper Indies Times, mimicking the way Grenadians accent their English to talk about "dese times" since the American invasion in October 1983.

Prime Minister Herbert Blaize professes to be worried that the Bishop followers could try to reassert influence through underground agitation or what he calls "making trouble." Despite the worry, visitors to his headquarters in St. George's Botanical Gardens can walk into his office unchallenged and present their business. True to their Caribbean civility, most knock.

On a hill above town, former prime minister Eric Gairy still refuses to accept Blaize's resounding victory in the island's Dec. 3 elections. The United States flew in altered ballots from Georgia, he maintains, and that is why Blaize's New National Party won 14 of the 15 seats in the House of Representatives.

"My political position is solid, always has been," Gairy insists. "I'll be prime minister of Grenada very shortly."

GAIRY WAS ACCUSED of black magic as well as political shenanigans until Bishop overthrew him in 1979. But he apparently has no connection to the problem travelers have encountered recently trying to cross Paradise Bridge along one of the island's main roads.

According to an article in another Grenadian weekly, the Informer, two trucks were pulled off the bridge and down into the river in recent weeks by a "jumbie," island slang for an evil spirit. Several persons ended up in the hospital from injuries received when their vehicles crashed off the structure, said the paper under the headline, "Jumbie in Paradise."

"Old people used to say that the river bridge in Paradise, St. Andrews, has more jumbie than in hell, but I never believe it until when it was proven by the truck drivers," said the unsigned report. "Truck drivers, other vehicle drivers, foot drivers and all other drivers, please try an don't be the next victims of that jumbie on Paradise Bridge, because it could be real dangerous."

IN GUADELOUPE'S main city, Pointe-a-Pitre, local gourmets like to brag about the Canne a Sucre restaurant, a gingerbread house that has become the island's top eatery, replete with pink tablecloths and heavy silver.

A recent visitor found, however, that the chef's qualities do not include zeal. Arriving at the dinner hour, the lone customer was urged to have an aperitif. After declining, he was urged to order wine. After he chose a bottle, the waitress -- also all alone -- served up a glass and admitted:

"I can't take your order yet because the chef has not yet arrived."

One hour and two telephone calls later, the embarrassed waitress said she was now authorized to take an order, because the chef, who lives upstairs and owns the place, was on his way down.

Soon the food arrived. And out from the kitchen also stepped the chef, splendidly arrayed in a traditional cross-buttoned white tunic topped off with a scarf around his neck. He and his wife sat to take their coffee, absorbing the waitress while the customer waited for his check.