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However, a president of the AVSNI said the message had nothing to do with the group.
"I can state categorically that The Australian Vaccination-skeptics Network Inc does not support or agree with the sentiments or messages portrayed in the picture," she said.
"We do not own the page it was posted on.
"What the Australian Vaccination-skeptics Network does support and believe in, is the right of ALL parents to make an informed choice in regards to vaccinating their children, whether they vaccinate, selectively vaccinate or do not vaccinate at all," she said.
"We are pro-choice, pro-information and pro-parental rights."
The new federal law, which was in part prompted by the death of one-month-old Riley Hughes from complications arising from whooping cough, means that parents who refuse to immunise their children are set to lose up to A$15,000 a year for every child when the changes come into force from January 1, 2016.
The post, which has since been removed, caused an instant outcry from followers and opponents of the group alike, with social media users labelling the post "tasteless", "disgusting", and a possible trigger for those who had suffered sexual assault.
"Dear rape victims, according to the rabid anti-vaxxers what you went thru is no worse than. Shame," said one social media user.
"Are you saying that your child being immunised is as bad as your child being raped? This could also be very triggering for victims of sexual assault," said another.
The administrator of the page defended the post, maintaining that is wasn't tasteless, but honest.
"What truly is tasteless is our elected government trying to tell us that we have to vaccinate our children even if we don't believe it is best for their health," the administrator wrote.
"That is tasteless. And if you find this post confronting - imagine how you would feel if you were a parent who was being told that they were going to have to vaccinate their children or starve."
Fiona McCormack, the CEO of Domestic Violence Victoria said the comparison was "so irresponsible and inappropriate".
"To compare a doctor injecting a child against something like the measles to rape ... it's obscene," Ms McCormack told The Age.
On Wednesday, a post to the page said that the controversial post was made by someone independent to the organisation.
"As written in the about section, the AVSNI has not owned this Facebook page for some time. This page is open to the public. We sincerely apologise for an earlier post that caused offense to many, including supporters. We are still investigating and have taken your comments on board," the post said.
The AVSNI has previously used the metaphor of rape to oppose vaccinations, when reports of a child being given a court order to be immunised was labelled by the group as "court ordered rape".
"Think this is an exaggeration? Think again. This is assault without consent and with full penetration too," the post said.
"If you were the doctor ordered to administer this vaccine and the mother was standing there, holding her child under a court order while you prepared the shot and she was begging you to stop and crying that it would hurt and you continued to do it anyway - how different is that from rape?" the administrator later commented on the post.
The Network has previously come under fire when it was stripped of its registered charity status last year.
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