CAPRI, Italy The ferry docked next to the blue Capri a Covid Free Island billboard and the residents and workers disembarked, carrying luggage and antibodies.

Among them was Mario Petraroli, 37, freshly vaccinated and ready for the grand reopening of the luxurious hotel where he works as director of marketing.

The big day, he said as he rode a funicular up above turquoise waters, terraced gardens dripping with lemons and winding cliff-side footpaths.

He reached the summit and stepped out onto a glamorous town famous for its Jackie O. and J. Lo sightings, exorbitantly priced Caprese salads, and reputation as a billionaires playground. Everyone around him the shopkeepers unpacking the Pucci, Gucci and Missoni garments from plastic bags, the bartenders sliding ice into Spritzes, the carpenters hammering finishing touches on the underground Anema e Core Taverna dance club had been vaccinated.

It is a different story on the Italian mainland, visible across the gulf from the belvedere rimmed with faux Roman columns. There the inoculation campaign has advanced unevenly, with many seniors yet to receive a first dose.

Its very frustrating, acknowledged Mr. Petraroli, whose 68-year-old uncle back home in Naples contracted the virus at the end of April as he waited for his vaccination appointment. He died days later.

That loss further convinced Mr. Petraroli that Capri should not wait around for Italy to get its act together. By then, he figured, the summer season would be over, and livelihoods, and possibly lives, would be lost.

The gruff president of the Campania region, which includes Capri, clearly agreed.

Feeling the heat from Greece and Spain, which had prioritized vaccination campaigns on their islands to lure tourists away from Italy, the president, Vincenzo De Luca, had diverged from the governments vaccination strategy of prioritizing categories of more vulnerable Italians. Instead, he treated Capri and other holiday islands as special cases.

He fast-forwarded vaccinations on Capri by flooding the island with doses. Seniors were inoculated first, then the middle-aged, then 20-somethings and even some teenagers while the rest of the region was still struggling to get shots to all its 70- and 60-year-olds.

Then Mr. De Luca vaccinated anyone who worked on the island.

Massimiliano Fedriga, president of the northern region Friuli-Venezia Giulia, warned that social tensions could flare if Capri, which had avoided outbreaks, and other islands received special treatment. The national government in Rome insisted that younger residents even on the islands should be vaccinated only after all the entire regions elderly and vulnerable were inoculated.

But Mr. De Luca persisted and the government, eager to reignite the economy, eventually came around. This month it approved vaccinating all residents of smaller Italian islands, from Elba to the Aeolians off Sicily. Even landlocked towns like the Sestriere ski resort in the Italian Alps have tried to get in on the fast-track inoculations.

Its time to book your holidays to Italy, Prime Minister Mario Draghi declared.

On May 8, as national vaccinations picked up, Mr. De Luca came to Capris famous piazzetta in the center of town to declare Mission Accomplished and to urge tourists to book their vacations on the islands.

Mr. Petraroli, the hotel marketing director, now crossed the same square, past copper-toned Capri enthusiasts who sipped and smoked, their faces pointed at the sun. He entered a warren of narrow streets, lined with Rolex outlets, brand name boutiques and Hangout, a popular pub in town owned by Simone Aversa.

My friends say, Oh lucky you, were still waiting, said Mr. Aversa, who is 30 and vaccinated. He said his family in Florence complained that they too live in a town supported by tourism; why was Capri getting such special treatment?

Capri is the answer to the question of why you and not us, Mr. Aversa said with a shrug. Because its Capri.

Mr. Petraroli pointed out the restaurant Aurora, Capris oldest. Its owner, Mia DAlessio, 49, that day had received both her second shot of the Pfizer vaccine and a call from Beyoncés manager, booking the usual private dining room for the diva and her husband, Jay-Z, in August.

The couple would be safe, she said, because everyone in her restaurant and family was vaccinated. That includes her daughter, 19, a tennis player who has trained with Andre Agassi and hit with Bernard Arnault, the French billionaire head of the luxury-goods giant LVMH Moët Hennessy.

Capri will be more jet set than before, Ms. DAlessio said in front of a wall of pictures including of her posing with Steven Spielberg, Mariah Carey and Michael Jordan. They come for the pizza of the jet set, she said. Its not too heavy. No yeast.

The VIPs, equipped with private jets, yachts and personal doctors, would, she said, have less trouble getting to the island than souvenir and Blue Grotto-postcard hungry hoards of day trippers flopping around in Capri sandals and limoncello stained linen shirts, especially because the cruise industry is struggling to return to full force.

Its a good season to experience Capri, said Mr. Petraroli as he reached the Capri Tiberio Palace, which Kylie Jenner repaired to in a recent summer after, workers at the port told him, she felt unwell on her yacht.

The hotel is named for Tiberius, who ran the Roman Empire from Capri, throwing people off cliffs and training Caligula how to have a good time. Many here call him Capris first tourist.

Mr. Petraroli said modern hedonists were already calling, sending scouts to make sure that the vaccine situation, and vibe, is what they want.

The real issue for them is once they are here, do they have something to do, he said as workers carried an espresso machine and dusted the blinds.

Upstairs, Mr. Petraroli opened the Suite Bellevue, booked mostly by sheikhs and sultans and very famous guys. It leads to a terrace tiled with hand-painted ceramics, topped with a Jacuzzi plunge pool. Mr. Petraroli said the late basketball star Kobe Bryant had such a special bond with our top suite that he named his daughter Capri after staying there.

Outside the room, Alessandro De Simone, 23, dusted crystal decanters filled with cognac and whiskey. Mr. De Simone, who is also vaccinated, said none of his friends back home in Naples had been.

From their perspective, he said. Im privileged.

But others on the island said their mainland friends saw them as luxuriously housed lab rats.

Domenico Marchese, 29, who prepared banana syrups for his signature Barbados Punch cocktail in the hotels Cuban-themed Jackie Bar, said that while his parents, in their 50s, couldnt get vaccinated, his friends, in their 20s, refused to.

Im trying to change their mind, he said. I tell them dont worry.

All around the island, which as recently as 2019 campaigned against overcrowding, the prevailing concern is that no one will come.

At the Augustus Gardens, lined with flower beds and graceful statues, there was no one at the lookout points to wait at the green tape markers reading, Wait Here. The crystalline water off the coast, usually clogged with ships, was nearly vessel free.

Giuseppe Maggipinto, 53, and the president of the islands oldest cooperative of motorboat owners (All our skippers and staff have been completely vaccinated! reads their website) sped uninhibited around the island. He navigated through the islands trademark Faraglione rock formations (This is where Heidi Klum got married on a yacht) and by La Fontelina beach club where three sunbathers, their knees bent and gleaming, laid under the cliff.

He lamented the hysterical polemics about us getting vaccinated, arguing that without a hospital, if there was a cluster here, we had nothing to save our lives.

He moored the boat back at the dock where more ferries brought a trickle of tourists, but also returning residents. Dario Portale, a local greengrocer, and his family, were among them.

The day after getting their shot, the couple left for Milan, in the countrys hard hit region of Lombardy, to introduce their 10-month-old son to his mother. She is 62, works in a post office and is not vaccinated.

Shes still waiting, Mr. Portale said.