For many Americans who were vaccinated months ago, the future is beginning to look grim. Frustration is straining relations even within closely knit families.

Josh Perldeiner, 36, a public defender in Connecticut who has a 2-year-old son, was fully vaccinated by mid-May. But a close relative, who visits frequently, has refused to get the shots, although he and other family members have urged her to do so.

She recently tested positive for the virus after traveling to Florida, where hospitals are filling with Covid-19 patients. Now Mr. Perldeiner worries that his son, too young for a vaccine, may have been exposed.

“It goes beyond just putting us at risk,” he said. “People with privilege are refusing the vaccine, and it’s affecting our economy and perpetuating the cycle.” As infections rise, he added, “I feel like we’re at that same precipice as just a year ago, where people don’t care if more people die.”