In that case, he was convicted of offensive behaviour and fined $800.
There has been widespread scrutiny of a legislative loophole allowing Arps to run for the board.
Former MP and educational researcher Dr Liz Gordon told John MacDonald on NewstalkZB that she thinks Arps is not a suitable person for the role.
Gordon wrote a blog post last night titled: Board of trustee rules not up to supremacist challenge.
She raised concern that there is nothing in the legislation about good character.
A commenter under the name Phil Arps left abusive comments on the post.
Gordon said there are rules in place if you want to work at a children's charity.
"You have to get yourself signed off as a fit proper person," she said.
Gordon said the rules around becoming a school board member only include having a child at the school and not being sentenced to longer than 24 months in prison.
She also questioned if he is standing to make Te Aratai a strong school or if it is to destroy democracy.
Christchurch City councillor for Heathcote Sarah Templeton, who has children at the school, said a grey area in the rules allowed him to run.
"The school has worked really hard to check whether he's eligible and it is a grey area, and that needs to change.
"Any member of staff or even parent helpers ... all need to have police vetting, and that's not the same for board of trustees' members, even though in high schools' cases, board of trustees have student reps on them."
Federation of Islamic Associations chair Abdur Razzaq said Arps was probably aware he would not get the position, but wanted to provoke a reaction.
"What we are seeing here is a trend ... which we've already seen in the US and it's being mimicked over here.
"That's deliberate."
Razzaq said there was a trend of white supremacists wanting take part in elections, such as boards of trustees, in order to bring their hate into the mainstream.
"They want to normalise hate, as you see it nowadays where people start talking about it as if it's something normal.
"Worse still, they want to create disharmony."
The tactics are aimed at provocation, he said. "It's not a one person trend, this is a trend around the country and around the world."
Legislation was one of a toolkit of measures identified by the Royal Commission of Inquiry to address this, he said.
Templeton would be very concerned if he was elected, she said, and had been in contact with other parents who were also worried.
"People are spreading the word that people really need to vote, because board of trustee elections are often really low voter turnout, even lower than local body ones."
The principal of Te Aratai College, formerly Linwood College, has confirmed Arps has put his name forward for one of five trustee positions.
The school is not far from Linwood Mosque, the other mosque targeted by the shooter.
Richard Edmundson would not say what he thinks of Arps being a contender for board a position but said there were nine people vying for election.
He said the school was known for its inclusion and diversity.
The election runs until September 7.
- Additional reporting, NZ Herald