Philip Arps was jailed for 21 months for sharing footage of the terror attacks. He put his name forward for a trustee position at Te Aratai College, formerly Linwood College.
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 she had been in contact with other parents who are 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."
Te Aratai College has more people standing than vacancies on the board, so those who put their names forward would not be automatically appointed, she said.
"I'm incredibly grateful that we have nine candidates for the five spaces on the board - and I know that other schools locally only had enough candidates to fill the vacancies."
Secondary Principals' Association president Vaughan Couillault said Arps appeared to meet the criteria because he was jailed for less than two years.
"But also the particular piece of legislation goes on to say that that person, if they have served their sentence, can then stand."
"The criteria at the moment in this particular instance seems to fall woefully short of what the general population would expect," he told Morning Report.
Couillault had not seen evidence of a trend of standing for New Zealand school boards to gain media attention, but it was a worry internationally, he said.
