Just a few decades ago, tens of thousands of people in Australia and New Zealand enthusiastically welcomed Queen Elizabeth II and other members of the royal family on tours across the two countries. But after her death last year, and with the two Eastern Hemisphere nations reckoning over their colonial histories, enthusiasm there is ebbing for a British royal family that increasingly feels like a relic of another age.

“There has been a fundamental change since the passing of Elizabeth, unquestionably,” said Craig Foster, the chair of the Australian Republic Movement, which campaigns for Australia to abandon the British monarch as head of state. He added: “People in Australia were so respectful that they didn’t really want to open up conversations, especially in the last 10 years of her life.”

With her son Charles now on the throne, the mood may be shifting, with more people in both countries calling for a republic in recent polls. But there also remains a sizable amount of support to keep Charles as the head of state, and plenty who seem unbothered by the issue.

“I do not care,” Laura White, a 31-year-old personal trainer in Auckland, New Zealand’s largest city, said of the coronation after a recent school run. “I’ve got bigger fish to fry, with the cost-of-living crisis in New Zealand.”

Few people were talking about the coronation in her workplace or community, Ms. White said, and her two children had not learned about it at school, where the greater focus was on Maori, the Indigenous people of New Zealand, rather than on the country’s colonial history. “The last thing they want to do is encourage talk about the queen more than the people they colonized in New Zealand,” she said.

Ms. White said that she would not actively push for a republic, but that she could see benefits to becoming one. In that respect, she is like Prime Minister Chris Hipkins, a lifelong republican who has also said that he would not seek to make that change for New Zealand.

“When New Zealanders are ready to have a debate about whether or not they want to become a republic, then I will just be one vote in that,” Mr. Hipkins told reporters in London this past week. “But it’s not something that I intend to prioritize — I don’t believe it’s the right time to do it.”

His Australian counterpart, Anthony Albanese, has said that a vote on whether Australia should become a republic is not imminent, and that he is focused on constitutional recognition for Aboriginal Australians. “A demand for another vote isn’t something that can be imposed from the top, because it won’t be successful,” he said in a televised interview.

Unwinding Australia and New Zealand’s relationship with Britain would require grappling with the legacy of colonialism, said Robert Aldrich, a historian at Sydney University. “The challenge is to try to get the balance between condemning the system but also trying to comprehend how complex that system was,” he said.

Still, the actual effects of that change would be negligible in many respects. “Becoming a republic, for most Australians, would make very little difference,” he said.

For some, Charles’s coronation is not simply irrelevant, but actively annoying, and a shift to republicanism could not come soon enough.

“As an Australian, I have absolutely no interest in this dysfunctional, archaic, parasitic institution,” said Karen Houghton of Brisbane, Australia. She added: “I have never subscribed to the existence and role of a monarchy. My uppermost interest in the British monarchy is to see Australia break away and become a republic.”

Damien Cave contributed reporting.