Edith Eglin, a summer resident since 1938 and the president of the Watch Hill Chapel Society, said: “I consider her coming here a big surprise and a pleasant one. Did it encourage people with preteen children to come here and buy houses? I don’t think so. Has there been increased air traffic at our little airport? I doubt it. Her plane is too big to get in here.”

To Mr. McBride, the architect, “Taylor Swift is an anomaly,” he said. “So she’s like our pet celebrity. Everyone has kind of adopted her and refers to her by her first name. She’s ours now. In a community like this, you either absorb or deflect.”

Ms. Swift’s Fourth of July party this year went unnoticed as it unfurled in real time. Watch Hill residents, like the rest of the world, experienced it after the fact, as a media event. In any case, it was quickly overshadowed by the latest chapter in the long-running feud between Taylor Swift and Kanye West, as Mr. West’s wife, Kim Kardashian West, took a swipe at Ms. Swift on her TV show last Sunday.

To briefly recap — stay with me here — Ms. Kardashian West then posted recordings of a phone call between her husband and Ms. Swift, in which it sounds as if Ms. Swift is giving her approval to the lyrics of Mr. West’s song “Famous,” an account that Ms. Swift quickly disputed in a statement on her Instagram account. (“Famous,” famously, says some nasty things about Ms. Swift.)

What does all this have to do with Watch Hill?

The way in which viral media works is through “generators and prompts,” like Ms. Swift’s July 4 Instagram photos, said Charlotte Cotton, curator of “Public, Private, Secret,” an exhibit at the new International Center of Photography museum in Downtown Manhattan, which examines how identity is tied to public visibility. Ms. Cotton saw a direct relation between Ms. Swift’s romping photos and Ms. Kardashian West’s leaked video, which she explained as a kind of celebrity brand smackdown.