The article was taken down after about a week, following a series of complaints by members.
Online, various party members described the article as transphobic and some have gone as far as to call it hate speech.
Others, meanwhile, came to Abigail's defence, both defending the content of the article, and on grounds of protecting free speech and opposing censorship.
The Herald understands the party's Rainbow wing had lodged a complaint, but requests for comment were not answered.
Te Awa is put together by a board of volunteers independent of the party's politicians. The editor declined to comment on Tuesday.
In a statement, a spokesman for the party said the board had apologised.
"We regret that the article was published without a response or right of reply from the affected community, and that our party policy wasn't made clear," he said.
"The Green Party upholds the value of diversity and inclusion and we want to reassure members of this."
A long-time member and former candidate for the Green Party, speaking on condition of anonymity, called for the board to resign to allow for fresh elections.
"They were … not sorry, didn't see a problem, that it would stay up, and felt we were overreacting."
The member said the inference trans women were not real women was offensive and "tremendously unfair".
"Trans people already struggle enough with not being able to have gender reassignment surgery without women being scared they're going to be sexually assaulted by them because they still have a penis. It can't get more bigoted than that."
Another member said she had resigned from the party over what she said was a lack of action, and that others had done the same.
The Herald has been unable to contact Abigail.
But speaking to Radio NZ, she denied the article was transphobic and said her arguments were being ignored by those opposed to them.
"My article listed the facts of what has been happening in countries where new legislation to ensure trans gender rights have confused gender with biological sex and is resulting in the loss of women's rights, and free speech on the issue being completely shut down," she said.
Abigail said some members of the Green Party had also resigned over its "anti-women" policies.
MP Logie took to Facebook, outlining the party's position amid the criticism.
"We have an urgent human rights challenge to realise the rights of trans and non-binary people," she said.
"I don't think it's in any way acceptable to suggest those rights threaten anyone else."
Greens co-leader Marama Davidson, also on Facebook, apologised for the harm caused by the article.
"We are actively working on resolving this," she said.
Both MPs declined to comment on the matter on Tuesday.