They are unhappy that Black Lives Matters posters were taken down and they say students are being isolated after speaking out.
Students say they were asked for their social media passwords and Wi-Fi was suspended.
A parent, Maria Marama, said families want to meet with the school and its board, not just the diocese, to address racism.
"Working with families to get something right for the students, particularly in terms of the racism that exists in the school," she said.
"It is clear from what the kids are doing today that not only is it about Black Lives Matter for them, but also about other things that need to change."
Students say they are upset at not having a voice at the school.
In a leaked recording of an assembly, school principal Raechelle Taulu can be heard saying it is her who took down the Black Lives Matters posters.
Student Tatenda Chivasa said there was no apology, only a defence of the school's actions.
"It was pretty disappointing, and kind of heartbreaking because we've leaned on the school for support and love as they preached all the time for four years. And it's just really sad to hear our school fall apart like this, and knowing that that trust is kind of broken," she said.
"I don't think they're handling this professionally, turning off the Wi-Fi from personal devices, taking people's Instagram passwords, telling them they can't post anything.
"Not apologising at assembly was just something else, and defending themselves instead of apologising - that offended a lot of people, when I came out people were just really upset. Not allowing parents to talk to the board, or email - that was just out of hand too."
Her mother, Ketina Chivasa, said the school was downplaying the matters raised and she had found it impossible to speak to the school principal or board.
"When they come here for those six to eight hours at school we expect them to be safe," she said.
"We don't believe our children are safe at the moment and for the ones who spoke up and who put the posters up, they are now being socially isolated around the school because they spoke up - so the moment you stand for the truth, you will stand alone. So that's why we [parents] said no girls 'You're too young, and we want to help you to carry this burden'."
The school declined to comment as the principal was not available.