A trustee at one of Britain’s top museum groups has withdrawn her reappointment application in protest at being asked to “explicitly express support” for the government’s policy against the removal of contentious historical objects.

Sarah Dry, an author on the history of science, warned in a letter seen by the Financial Times that bowing to these conditions would ultimately harm the Science Museum Group’s reputation, compromise its board and “betray the trust of the public”.

“Any requirement which seeks to constrain the independent curatorial and interpretive work of national museums violates the long-established principle of arm’s length bodies,” she wrote to the group’s board and chair Dame Mary Archer. “Today it is contested heritage. Tomorrow it may be another issue. This has several damaging effects.”

Her objections reflect mounting concerns in the arts sector over Boris Johnson’s systematic drive to reshape opinion on the boards of museums, galleries and media groups by easing out dissenting voices and appointing trustees more aligned with government policy.

It follows the decision by Sir Charles Dunstone, the billionaire founder of Carphone Warehouse, to quit as chair of the Royal Museums Greenwich after ministers blocked the reappointment of one of his trustees.

Oliver Dowden, culture secretary, outlined the government position to “retain and explain” contentious statues and works in a letter to arm’s length bodies in September, adding a warning against “activism or politics”.

Dowden, who has the strong support of Downing Street, is convinced that these public bodies, largely reliant on taxpayer funding, would benefit from an influx of new, diverse talent that better reflect the views of the country.

To date, the culture department has taken a more aggressive approach to limiting trustees to one term and, in a break with past practice, requiring candidates to pledge support for the government’s “contested heritage” policy. Guidance for trustees, issued in March, also urges them to “consider the broader mission and duties of your sponsoring secretary of state”.

An ally of Dowden said it was “entirely proper to expect trustees and the institutions that they are responsible for to respect established and agreed government policy”, adding: “As temporary custodians of our heritage, trustees should work to preserve our heritage and use it to explain all aspects of our history.”

Some chairs and trustees have accepted Dowden’s more prescriptive approach to appointments, with several new appointees giving assurances of support.

But others fear the opinion-vetting will undermine the whole purpose of giving arts boards some independence from government in sensitive decisions about collections. Several trustees have considered resigning over what they see as a purge of critics, which has included government officials scouring candidates’ social media posts for evidence of disloyalty.

One trustee at a major national collection described it as a “total scandal”, saying it forced board members to “make judgments based on government policy rather than looking at whatever evidence is before them”. Another prominent trustee said they were “very uncomfortable” about the approach.

The Science Museum Group includes the Science Museum in London, the Science and Industry Museum in Manchester and the National Railway Museum in York — venues that, before the pandemic, attracted close to 5m visitors a year.

Archer, the scientist who has chaired the group since 2015, described Dry as “a valued and conscientious trustee”, adding: “She made a particularly strong contribution to the work of our collections and research committee, and I was sorry she decided not to seek a second term.”

The culture department said: “There is no automatic presumption of reappointment, and indeed, in the vast majority of cases, fresh talent is added with new appointments made.” Guidance for trustees of public bodies makes clear “they should act to deliver the outcomes expected by sponsor departments, ministers and ultimately the public”, it added.