And they argue that many in the Muslim community do not trust the police because of the way they were treated before and at the time of the Christchurch attacks.
But Mcclintock's lawyer rejected the conflict of interest claims and said the families' mistrust does not disqualify Mcclintock from the role.
Coroner Windley stressed the families' application does not allege misconduct, and any decision to remove her does not imply there has been any.
Hampton KC argues Mcclintock could be 'loath' to apply scrutiny to police
Counsel for some of the families, Nigel Hampton KC, argued a fair-minded member of the public could perceive Mcclintock has a conflict of interest.
"That the counsel assisting coming from such a background might be loath to put proper scrutiny on, not only individual officers ... but on the institution of the police itself, and its structures, its command, it's policies and procedures."
Inquisitorial vs adversarial
Coroner Brigitte Windley pointed out that coroner inquiries were inquisitorial, an attempt to establish facts, and not adversarial or seeking to find parties liable.
Hampton agreed but said that police actions would be subject to considerable scrutiny during the inquiry.
He repeated that a fair-minded member of the public might perceive Mcclintock's ongoing relationship with the police could make her "pull her punches" towards them in any finding the inquiry makes.
Hampton said the administration of justice at all levels should be free of the potential tainting influence of the perception of conflict.
And he said the Coroner's decision on Mcclintock's continued role could set a precedent.
He noted there was still no clarity about what Mcclintock's role and responsibilities at the inquiry were.
Some families feel police hostile towards them - lawyer
Hampton said the coronial inquiry needed to closely at the "actions, the reactions, the lack of actions of individual officers - and of the police as an institution leading up to, during, and after the 51 deaths".
The lawyer of other families Aarif Rasheed told the hearing the community felt the police and other authorities took a "securitised approach" towards them.
"The experience of the communities with the state has primarily been ... one of being seen as a threat to the public rather than being at risk in terms of their own safety," Rasheed said.
He said the Royal Commission acknowledged in its report that despite the mosque being attacked by white supremacists in the years preceding the shooting, it was the mosque and the community that ended up being "monitored".
"This mistrust ... between the families and the process does not arise out of a vacuum."
Hampton said some families say they were treated with hostility by some officers on the day of the attack.
'An allegiance and a loyalty to the state'
Meanwhile, Rasheed said there has been increased public awareness about the entrenched relationship between the Crown and Crown Solicitor, Meredith Connell.
He noted a "number of miscarriages of justice" in recent times where there appeared to be a "very strong loyalty" between the Crown Solicitor and police.
"That familiarity can breed a sense of complacency which may well have resulted in what appears now to be a pattern ... [of] quite well known, in particular, miscarriages of justice for people who are ... not Pākehā.
"We are talking about here really an allegiance and a loyalty to the state at the expense of other ... less powerful interests."
Mcclintock's solicitor responds
Mcclintock's solicitor Michael Hodge said the depth of the families' mistrust must be given some weight, but it could not by itself require her to be removed from the role.
That would be contrary to previous court rulings, he said.
Hodge said it was wrong as a matter of law to characterise her as having a conflict of interest.
"A conflict of interest in litigation is where counsel acts for one party against another party for whom counsel also acts - or has some other disqualifying relationship."
He said conflict did not apply because the [coronial] court was the decision maker, it was not party to the litigation.
"Ms Mcclintock is not acting for a party in this proceeding, nor is she acting against any party in this proceeding - that's not her role."
She was purely there to assist the court, and hers was not an adversarial role, he said.
Hodge noted she had no more special knowledge of police operational matters relevant to the inquiry that any other experienced lawyer would have.
Crown Solicitors have for many years done the same role that Mcclintock has taken on, he said.
