The first post, on July 26, by a contributor and edited by another person, had been removed from website but the other one, on August 1, in which Churchman is the author, remained.
She said the posts had "caused a great deal of stress and anguish to myself and the other elected members".
Elected members had a set of standards they were expected to adhere to including "avoiding conduct which is aggressive, offensive or abusive or which may constitute unlawful or inappropriate behaviour including sexual harassment".
Moreover the Health and Safety at Work Act 2015 stated one of its main purposes was to "protect workers, including elected members, and other persons against harm to their health, safety and welfare by eliminating or minimising risks", she said.
She was convinced she had made the "right stand" and hoped by "standing up against such behaviour" it would be "stubbed out in our community".
District wide councillor Jackie Elliott, who attended the meeting, which saw a security guard stationed at the front door, said, "Publishing offensive material about your colleagues is not acceptable in our workplace, in this workplace, in any workplace and I ask members of the community board to use your voices and your votes to say 'it is not ok'."
Churchman attended the meeting but wasn't allowed to speak by chairman James Westbury.
Notes from a speech Churchman wanted to read out said resigning was one of the hardest decisions he had made but he was "tired of the culture of bullying in the council aimed at those who speak out against its intentions".
"I'm tired of falsehoods such as the allegations of racism and sexism levelled at me by Cr Prvanov.
"I'm tired of trying to get Waikanae needs across to councillors who are so ignorant they do not even know what satire is.
"The final straw was the refusal of the chief executive to withdraw an improper notice of motion tonight where I'm attacked for something I didn't write or edit.
"I'm unable to effectively work in such a toxic atmosphere where lies are treated as facts and facts as lies.
"The personal abuse, including vicious comments from certain councillors, and the stress it causes, makes life in this environment unbearable."
Churchman's resignation means a by-election will be held to fill the vacancy.
"We will be calling for nominations for the vacant Waikanae Community Board position shortly," Kāpiti Coast District Council electoral officer Katrina Shieffelbein said.
"Community boards are an important part of local democracy and we encourage anyone who has an interest in representing the interests of, and advocating on behalf of, the Waikanae community to get in touch with the council."
"Electoral rolls will be made available at council service centres for electors to check they are enrolled and their details are correct."
The Waikanae Community Board covers an area from Waikanae Downs in the south through to Peka Peka in the north, bordered by mountains to the east and the sea to the west.
