The controversial article, published by LGBT's PinkNews, recently speculated a photo of the four-year-old prince with his hands on his face in a helicopter in Germany last month had made him a new symbol of gay pride.
He called on PinkNews to immediately withdraw the "misjudged" article and apologize.
PinkNews chief executive Benjamin Cohen said the feature was tongue in cheek, based on the comments of "hundreds" of social media users and that he had no intentions of removing the article at the request of Allister who, he said, opposed lesbian, gay, bisexual and transgender people.
The original article, by Josh Jackman, was published on 25 July with the headline: People think Prince George looks fabulous in this new photo.
It was published after a picture was taken of the little prince, with an innocent, delighted, expression on his face, as he stood in a helicopter (above) one day shy of his fourth birthday.
The article reads: "Prince George has become a gay icon overnight - at least, that's what some people - sorry, his subjects - are saying on Twitter".
But Jim Allister, party leader of the Traditional Unionist Voice (TUV) has blasted the article "grossly offensive", saying "sexualising a young child in this fashion is entirely inappropriate".
'In reality, the photo which prompted the piece shows a four-year-old boy who is smartly dressed and excited about being on a helicopter with his male father and female mother.
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In a scathing letter of complaint, he demanded the story be removed and an apology from the site, "To take an image of a little boy and to fantasise of him being an icon for a life defined by sex is outrageous and sick", he said.
But these claims have been strongly rejected by some, including Ireland politician Jim Allister, who described the article as "outrageous and sick".
"Allister is not an impartial commentator on this issue".
"Mr Allister also appeared to claim that being gay is a "life defined by sex".
"Mr Allister's letter contains a number of concerning points".
But the publication's chief executive pointed out that PinkNews could not be a member of IPSO as it was a "digital media company", and not a newspaper or a magazine.
"As Madonna, Lady Gaga, the Babadook and yes, even Ariana Grande have shown, you don't have to be gay or even have a defined sexuality to be an LGBT icon". He opposed the decriminalization of homosexuality and was the only member of the Northern Irish Assembly to oppose pardons of gay men convicted of offences that would not be crimes today.
While the story was no longer on the website's homepage, it would remain on the internet, he said.