NEW YORK — Ask the CEO and president of the Metropolitan Museum of Art whether he’s accepting money from the Sacklers, the billionaire dynasty notorious for its ties to the drug company Purdue Pharma, and the answer is somewhat complicated.

For one thing, it depends on which Sackler.

“There are people who have the name ‘Sackler’ who have nothing to do with the Purdue Pharma situation,” Daniel H. Weiss says. “If it’s someone tied up with the leadership at Purdue Pharma, we step away.”

Purdue Pharma recently filed for bankruptcy as part of a plan by the maker of OxyContin to settle thousands of lawsuits from state and local governments over the nation’s opioid crisis. The Sacklers, who own Purdue, were listed by Forbes magazine in 2016 as one of the 20 wealthiest families in the U.S. and have contributed money to cultural institutions around the world.

The family has pushed back against accusations that Purdue played a central role in the deadly epidemic, but the legal battles have led some to sever ties with the relatives. The allegations have also heightened a debate over how much museums should rely on the support of the rich and what, if any, conditions should be imposed on their gifts.

Cars pass Purdue Pharma headquarters in Stamford, Conn. AP Photo/Frank Franklin II, File

For museums in the U.S. especially, where private funding can account for more than three quarters of an annual budget, the decision to cut off a wealthy contributor such as the Sacklers or Jeffrey Epstein is sometimes a choice between upholding their stated values and being able to communicate those values through the art they champion.

“We live in populist times, with more awareness of economic and political inequality and more scrutiny of the wealthy,” says David Callahan, author of “The Givers” and founder of the online site Inside Philanthropy. “This greater scrutiny is overdue, but it’s creating lots of anxiety in nonprofit institutions with strong ties to America’s far upper class.”

Over the past year, the Tate museums in London and the Guggenheim in New York are among those that announced they would no longer accept money from the Sacklers. Other institutions have not entirely distanced themselves, citing legal reasons and other factors.

Last spring, the Met announced it would no longer accept gifts from Sackler family members closely connected to Purdue Pharma, but would allow for donations from those not involved. (Various Sacklers have denounced Purdue Pharma and called for some form of atonement).

The Met is not renaming its Sackler Wing, because, Weiss says, it’s contractually obligated. In Washington, the Smithsonian Institution rejected calls to remove the Sackler name from the Arthur M. Sackler Gallery, which opened in 1987 after Arthur Sackler (who died the same year) donated more than 1,000 works of Asian art and millions of dollars for construction.

In a recent statement to The Associated Press, the Smithsonian said the gallery was named in “recognition of Sackler’s generous gift” and that the donation agreement requires the Smithsonian to keep the name in “perpetuity.”

The Smithsonian added that it is no longer “seeking” money from the Sacklers and that in 2011 it changed its gift policy so that a name could be changed after 20 years or when a space gets its next major renovation.

Smithsonian chief spokeswoman Linda St. Thomas said control over exhibitions “rests solely with the Smithsonian” and that all gifts over $1 million are reviewed by leadership and approved by the Board of Regents.

Harvard University, where protesters have demanded the school rename the Arthur M. Sackler Museum, also cited contractual reasons for keeping the name and said that the Sacklers donated money before the development of OxyContin.

Philanthropy has a long history of conflict in the U.S., dating back to when steel magnate Andrew Carnegie spent vast amounts of money on libraries, schools and other educational facilities even as his workers protested their low wages.

More recent examples include the University of Southern California School of Cinematic Arts, which rejected $5 million from Harvey Weinstein, and Chicago’s Field Museum, which divested its financial portfolio from fossil fuels.

The definition of a toxic donor “is vague and keeps changing,” Callahan says. He cited the resignation of Warren Kanders from the board of the Whitney Museum after protests about his company’s sale of tear gas used at the U.S.-Mexico border and elsewhere. Previously, Kanders’ business had not been grounds for being pushed off the board.

“But in this highly charged political climate, the way a wealthy individual is seen can change rapidly,” Callahan said.

Weiss wonders if the Met would now accept money from Carnegie or fellow tycoon John D. Rockefeller, both infamous for their monopolistic business practices. The Met has received millions from controversial donors, notably David H. Koch, who died last month. Koch and his older brother Charles were leading right-wing benefactors reviled by environmentalists and others for casting doubt on man-made climate change and opposing efforts to fight global warming through reducing greenhouse gas emissions.

David Koch was on the Met’s board of trustees and contributed $65 million to a renovation of the plaza in front, named David H. Koch Plaza by the Met in 2014. The museum at the time defended the decision, which led to protests, saying it was a fitting honor for Koch’s “generosity and level of commitment.”

The Met does not “administer a partisan test for our donors — rather we accept gifts from those who seek to join in advancing our mission,” Weiss said.

“It’s equally important,” he added, “to recognize that gift acceptance administration requires continual review … as the landscape of cultural values, laws and facts change, and a bright line is often an imprecise instrument.”