The National Trust has warned of the damage it faces from what it calls an ideological campaign waged against it by self-styled “anti-woke” insurgents whom the charity has accused of seeking to stoke divisions.

It was prompted to speak out as members raised concerns about a range of “extreme” positions taken by individuals involved in a group called Restore Trust, which is backing a slate of candidates in elections for the NT’s governing council.

The group, which has been heavily promoted in the pages of the rightwing press after its foundation and has spoken of building up a “fighting fund” of tens of thousands of pounds, is also now using paid-for social media adverts to try to influence the election.

The trust – one of Britain’s biggest land owners – also fears for its carbon neutral policies in the face of the challenge by the Restore Trust (RT), which it says is waging a culture war on a number of fronts.

RT’s directors include a financier who has backed a leading climate-sceptic lobby group and currently chairs another.

Members of the charity have also expressed particular concern about RT’s endorsement of Stephen Green, the leader of a Christian fundamentalist lobby group, for one of six vacant positions on the trust’s governing council.

Green, who accuses the NT leadership of being “obsessed with LGBT issues”, has lobbied against the criminalisation of marital rape and defended overseas laws proposing the execution of some gay people.

“Our founders set out to protect and promote places of historic interest and natural beauty for the benefit of the nation. That means we are for everyone. Whether you’re black or white, straight or gay, right or leftwing,” an NT spokesperson told the Guardian.

“We have always debated openly and freely to overcome differences of opinion, and paid-for campaigns that back candidates with ideologies opposed to our values are new and would be concerning for any charity.”

They also addressed one of the original flashpoints for why RT said it had been set up – the notion that there was widespread anger among members about a report the charity published last year showing connections between 93 of its historic places and colonialism and slavery.

Properties include Winston Churchill’s country estate Chartwell, because of his political roles and opposition to self-governance in India, and Lundy in Devon, where convicts were forced into unpaid labour.

“It’s right that we are open to public scrutiny. Our national institutions need healthy and respectful debate if they’re going to thrive and be handed on to serve future generations, as they have served so many in the past and present. They must not be used as a punchbag, to divide people, or led by extreme views.”

RT’s directors include Neil Bennett, the chief executive of RT2021, a company handling what he said was “the significant and growing amount of donations that have been provided to Restore Trust”.

“I agreed to take the role since I, like others, believe the National Trust’s management has lost its way and is failing in its duty to protect Britain’s heritage and present it properly,” he said, adding that he was concerned that the NT was undemocratic and prevented members from having a proper say in its affairs.

Supported by Sir John Hayes, the chair of the Common Sense Group of Tory MPs – which has sought to push the government in a more hardline direction on a range of “culture war” issues – RT has used hashtags such as #empirestrikesback and presents itself as a grassroots movement of more than 6,100 current and former NT members.

There are more than 5.5 million members overall, though only 0.5% typically vote at AGMs. The National Trust will hold this year’s AGM on 30 October.

As well as Bennett, RT’s “Meet the Team” page lists Neil Record, a City currency manager and past Tory donor who has given money to a climate denier lobby group the Global Warming Policy Foundation. He is chair of Net Zero Watch, a new campaign group which was launched this month and which seeks to “highlight the serious economic and societal implications of expensive and poorly considered climate and energy policies”.

By contrast, the National Trust has a range of policies designed to reduce carbon emissions and has been putting pressure on the government by supporting the Climate Coalition, a group of 100 organisations asking members to sign a petition demanding immediate government action.

Record told the Guardian that he had joined RT out of concern with the direction of the National Trust, as a lifelong member.

On climate change, he said that he became concerned a decade ago about what he described as “the shrill and intolerant quality of the debate” and that legitimate questions in respect of climate science were not being addressed.

“Instead, a new orthodoxy began to make any debate impermissible. I regard this an a very dangerous route for a democracy to take,” he said.

Green said he had no connection with Restore Trust but was grateful for their support. He referred to his statement to NT voters, in which he referenced the backlash among some members against a film by the National Trust which revealed that Robert Wyndham Ketton-Cremer, who bequeathed Felbrigg Hall to the nation, was gay. Green said he was committed to ensuring “that future donors feel safe from the Trust poring over their past and inventing salacious details of an imagined private life”.