A woman who did not want to be named told RNZ drag king Hugo Grrrl's Rainbow Show was interrupted by men wearing "Man Up" tshirts.
It was scary and doors had to be locked, the woman said.
"In the room were toddlers, there was like a three-month-old baby, and halfway through the show we started to hear yelling and then this distant banging of the doors on the room that the performance was in.
"And children and parents started to get frightened and we were all looking at each other."
"I went to the back of the room to make sure it was locked and the people from Pride, I think, assured me it was impenetrable. But the people outside started doing a really loud haka and kept banging."
The woman said Hugo carried on with the show before children realised something was wrong and started to feel unsafe.
She said parents had to comfort some of them.
"I called the police from inside as did a couple of other parents. I really did feel like they were trying to get inside and it felt very violent.
"It was a small children's event and it was crazy".
She said the audience had to wait until the police had cleared the premises before they could leave in single file.
"It was terrifying," she added in an email.
Police said they responded to a report of a disorder at an event in a public building on Te Atatu Road, reported at around 12.30pm.
They dispersed the group responsible for the disorder and no injuries were reported, police said.
RNZ has approached Auckland Pride for comment.
Another Pride event, Pride Elevates Presents: What Happened To Mary-Anne? scheduled for Q Theatre Saturday night, has been canceled due to "unforeseen circumstances," Auckland Pride announced on Facebook.
Destiny Church Leader Brian Tamaki posted on Facebook about the protest that he was "proud of my people who are out in the community today, making a stand against the Woke Agenda plaguing our city."
"Our West Auckland team are outside the council library in Te Atatu today protesting yet another drag king, Hugo, who is attempting to seduce more kids into their Queer lifestyle through their storytime events."
Auckland Council's Director for Community Rachel Kelleher said the council was very disappointed in the "non-peaceful" protest.
"The council is extremely disappointed in the non-peaceful actions of protestors attending today's rainbow-friendly educational event at Te Atatū Library, focused on the science of rainbows for tamariki.
"Our libraries and community spaces are provided as safe and inclusive places for the whole community, and any actions that intimate and threaten our community and staff will not be tolerated.
"The council respects the right for peaceful protest, but this was not that, and the protestors did not respect the staff or other users of the centre."
Another event planned this afternoon by Hugo Grrrl at the New Lynn Community Centre was canceled, she said.
"Due to the protest group shifting their attention to a planned New Lynn event, and based on the earlier behaviour, the council proactively cancelled this afternoon's event."
Te Atatū MP Phil Twyford said most members of his community did not agree with the ideology of Destiny Church, and the group's actions infringed on other people's right to freedom of speech.
"It's also the kind of bullying and bigoted behaviour that we just don't need in this community or in New Zealand," he said.
"I don't think that's where the great majority of people in my community, in West Auckland, I don't think that's where they're at. I don't think they like that. We're a community that embraces diversity."
Twyford said people at the event felt intimidated and threatened, which was unacceptable. He wants his community to take a stand.
"The community really just needs to say to Destiny Church, 'Man up, don't be personally threatened by drag queens reading stories to kids in a public library - get a life'."
