They are also seeking an interim order to prevent Kellie-Jay Keen-Minshull - also known as Posie Parker - from entering New Zealand until the review can take place.
Immigration New Zealand looked into her visa-waiver status after neo-Nazi groups attended her events in Australia earlier this week.
Keen-Minshull from Britain is holding rallies in Auckland and Wellington this weekend, after the Government decided she did not meet the threshold to be classed an excluded person.
Gender Minorities Aotearoa, InsideOUT Kōaro and Auckland Pride have filed for a judicial review in the High Court.
OutLine Aotearoa and RainbowYOUTH were also supporting the action to keep Keen-Minshull out of New Zealand, saying they had concerns for the immediate safety of trans people and the longer-term impacts of the stress, fear and anxiety her visit would cause.
Gender Minorities Aotearoa executive director Ahi Wi-Hongi said the groups believed Keen-Minshull's presence in New Zealand would pose a significant threat to public order and a risk to public interest.
"The facts in this case are clear, and the Minister's failure to act is putting our communities in danger. We are not opposing freedom of speech, we are opposing the measurable threat to public order and the safety of transgender people."
Auckland Pride director Max Tweedie said they were determined to challenge the decision, to protect Aotearoa's trans, non-binary and takatāpui communities.
The organisations said they expected legal costs would be minimal, but there was always a risk of escalation - and sought donations through a givealittle page.
Any surplus would be used to continue advocating for the rights and wellbeing of transgender and rainbow communities, they said.
In a statement, Immigration New Zealand general manager Richard Owen said yesterday: "I can confirm that Immigration New Zealand (INZ) has now finished reviewing the case involving Kellie-Jay Keen-Minshull.
"After reviewing all publicly known information about Ms Keen-Minshull and seeking advice from other agencies we have concluded that there is no reason to believe that she is, or is likely to be, a threat or risk to the public order or public interest."
The Immigration Minister said yesterday the he condemned Keen-Minshull's " inflammatory, vile and incorrect worldviews" and stood alongside New Zealanders who used free speech against those who wanted to take society backwards, but the assessment was she met the criteria.
"Like many New Zealanders I would prefer it if Kellie-Jay Keen-Minshull never set foot in New Zealand. I find many of her views repugnant, and am concerned by the way in which she courts some of the most vile people and groups around including white supremacists," he said in a statement.
"The decision on whether to suspend her NZeTA sits with Immigration New Zealand and they have assessed that she meets the criteria set out in the Immigration Act and regulations. This assessment took into account the events in Melbourne that occurred last weekend. I have been advised that this case does not meet the threshold for ministerial intervention.
"As we look towards her events for this coming weekend, the welfare and safety of our transgender community is front of mind. Event organisers maintain the primary responsibility to ensure they run a safe and secure event and police have advised they will also be in attendance to ensure public safety."
