As co-leader of the Scottish Green Party, Lorna Slater attended three official ceremonies honoring the death of Queen Elizabeth II, including her state funeral.

But she won’t be going to the coronation of King Charles III.

Paying last respects to a widely revered queen was one thing, she said, even if the funeral seemed at times “like a film set from ‘Game of Thrones.’” But a lavish coronation ceremony for King Charles, Ms. Slater said, is “absolutely repellent when you have families who can’t afford to feed their kids.”

With the crown passing from Queen Elizabeth to her less popular son, Britain’s monarchy faces a test throughout the country, but nowhere more than in Scotland. Pro-independence sentiment has long simmered there alongside ambivalence about the royal family: affection in some quarters, frustration in others and, maybe most troubling for the monarchy, a growing indifference.

In one poll, almost three-quarters of people questioned in Scotland said they did not care about the coronation, and less than half thought Britain should continue with a monarchy. In interviews, some Scots echoed Ms. Slater’s worries about the cost-of-living crisis rippling through British homes but while some lamented the inequality symbolized by the crown, others said the royals were part of national heritage and helped drive business.

According to John Curtice, professor of politics at the University of Strathclyde and Britain’s leading polling expert, surveys in Scotland show support for the crown around 10 to 15 percentage points lower than in England, in part because of the country’s big, polarizing constitutional debate over Scottish independence.

“Scotland is different, and a nontrivial reason as to why Scotland is different is that people who are in favor independence tend to be opposed to the monarchy,” he said.

“The crown is a British institution and people who don’t want to be part of the United Kingdom tend to say, ‘No, we don’t want that, thank you very much,’” he added.

Scotland does not appear close to another decision about independence. In 2014, Scots voted to remain part of the United Kingdom, and prospects of a second referendum — one that might open the door to an independent republic — have receded recently, amid a financing scandal engulfing the pro-independence Scottish National Party, which leads the government in Edinburgh.

Still, there are signs of a debate stirring. Addressing around 70 opponents of the monarchy at a recent event, Ms. Slater said that on coronation day, May 6, she would attend a rally for a Scottish republic in Edinburgh alongside her party’s other co-leader, Patrick Harvie.

At the same event he, too, spoke about spurning an invitation. “I told them I was washing my hair,” the shaven-headed Mr. Harvie said to loud applause.

John Hall, the treasurer of Our Republic, an anti-monarchy group, described Charles as “unpopular” and the new king’s scandal-hit brother Prince Andrew as “hated.” He added that, for opponents of the crown, “things are moving in a positive direction.”

Perhaps more worrying for the royal family is the indifference picked up by opinion polls, particularly among young people. Glasgow has had no applications to shut roads or issue temporary entertainment licenses for coronation street parties, according to the Scottish media.

The Scottish government will be represented at the coronation by Humza Yousaf, who recently succeeded Nicola Sturgeon as Scotland’s first minister, following her surprise resignation as S.N.P. leader.

But while his predecessors were careful to avoid alienating independence supporters who favor the monarchy, Mr. Yousaf describes himself as a republican.

Until the dates clashed with the coronation, he had planned to attend a pro-independence rally in Glasgow organized by a group called All Under One Banner, which recently described Charles as “Not Scotland’s King.”

Even Kate Forbes, the more socially conservative runner-up to Mr. Yousaf, sounded ambivalent in a TV debate in March. Asked whether she would prefer King Charles or Andy Murray, the Scottish tennis star, as head of state for an independent Scotland, she said, “In the long term I think that’s a question for the people of Scotland but I’m a big fan of Andy Murray.”

The royal family retains strong ties to Scotland, however, and when Queen Elizabeth died at Balmoral Castle, an estate in the remote and spectacular Scottish countryside that she loved, some believed that she chose to end her days there to help bind her realms. Tens of thousands of Scots paid their respects as her coffin traveled to Edinburgh, where it lay in state before being flown to London.

Royalists in Scotland consider the monarchy just as Scottish as English. In 1603, following the death of Elizabeth I, James VI of Scotland succeeded her, becoming James I of England. A formal union took place a century later in 1707.

In Ballater, near Balmoral, several events are planned to mark the coronation, including a ball, a concert, a pipe band performance and a picnic.

Wendy Cobban, who runs the Brakeley Gift Room with her husband and has helped organize the celebrations, said the royal family took an interest in the community and were vital to its economy. “They keep us all in a job, let’s face it, either working in Balmoral or the estates or those who benefit from the tourism that it attracts,” she said.

Across the road at H.M. Sheridan butcher’s, the co-owner John Sinclair was selling a commemorative coronation sausage, with pork, plums, ginger and hoisin sauce.

“It’s got a sweetness, but it’s got a kick with the ginger at the end, so it’s a nice sausage,” said Mr. Sinclair, who supplies Balmoral Castle, has met many royals, including the king, and counts Princess Anne among his occasional customers.

“She’s partial to a smoky pork sausage,” Mr. Sinclair said.

Locals tend to leave visiting royals relatively untroubled. “If they do come, I just treat them as normal, I am not up for bowing and scraping,” said Delane Morrison-Wallace, the manager of Treehouse gift shop. She said she had reservations about the monarchy but saw benefits, too: “I get that it’s a ridiculous concept — of course I do — but I do see that they do a lot for charities and causes and little places like this.”

In Glasgow, the mood is mixed, reflecting generational divides and the city’s history of religious differences, which are still expressed to some extent in support for rival soccer teams: Celtic (traditionally Roman Catholic and anti-monarchy) and Rangers (Protestant and favoring union with England).

At the Bristol Bar, where many Rangers fans gather, the owner Greg Wylie plans to encircle the building with giant British flags on coronation day.

Mr. Wylie said that sectarian divisions had greatly diminished over decades, but that the team retains a distinctive identity. “We are a British club, which doesn’t make us any less Scottish — we oppose all talk of independence,” he said. “Charles has taken over, we will just continue, we will have a day for his coronation and take it from there.”

A few miles away at a city center mall, William Russell, a retired landscape gardener, praised the king as an ambassador for the nation and said he planned to watch the coronation, expecting “a spectacular event.”

But outside, Charlize Ellis, a 19-year-old student, said she had little time for a monarchy, calling it irrelevant to her generation.

“I don’t care that much for the royals,” she said, adding that there was a glaring contrast “when you see things like the king’s coronation while people are struggling to heat their homes.”

Asked about her coronation day plans, Ms. Ellis was unable to say. “I don’t even know when it is,” she said.