“The museum deeply respects the work and views of scientists — both those who work as colleagues at the museum and those from the broader scientific community,” the museum said in a statement to The New York Times. “We also respect and understand scientists’ role in society, including adding their voices to political debates that relate to scientific issues.

“The museum itself, however, does not make appointment decisions concerning staff or trustees based on political views,” the statement continued. “The museum has long maintained that its funders do not shape its curatorial decisions.”

A spokeswoman for Ms. Mercer did not return calls seeking comment.

Whether cultural institutions should consider the personal and political allegiances of their contributors remains thorny territory, particularly since nonprofit organizations can rarely afford to turn away generous donors like the Mercer family.

Such questions were raised recently in connection with reports linking the Sackler family, prominent cultural donors, to the company that produces OxyContin, the powerful painkiller that has been involved in opioid overdoses. And some objected to the renaming of the Metropolitan Museum of Art’s fountain plaza after the conservative philanthropist David H. Koch in 2014 (he gave $65 million).

“A political litmus test for who should serve can be very destructive to a nonprofit institution,” said Reynold Levy, the former president of Lincoln Center. “As long as the mission and important portions of the program are supported by the trustee, what they do in the political world shouldn’t be relevant.”