Nigel Dawson, Portadown District Master for the Orange Order, told The Nolan Show he was in "disbelief" listening to Collins on Good Morning Ulster.
Dawson called for Collins' resignation, adding that her position is "untenable" and that she "must take responsibility".
"[The Parades Commission] doesn't command the confidence of the loyal orders," he said.
"They don't command, I think, the confidence of the greater unionist community."
Dawson said the commission is "no longer fit for purpose", and that the reputations of those on the committee "are in "tatters".
"They cannot class themselves as independent," he added.
Dawson said he has contacted the Secretary of State, Sir Chris Bryant, to request a meeting.
LISTEN: Parades Commission chair tells Good Morning Ulster she won't resign after High Court Drumcree case
LISTEN: Orange Order District Master calls for Parades Commission resignations on The Nolan Show
The Social Democratic and Labour Party leader Claire Hanna said the mistakes made by the commission "were a complete mess", but that it should not mean people "ignore the progress of the last 25 years".
"Residents have a right not to be intimidated."
However, Hanna added that "there will be resignations, and there should be resignations" within the commission.
Traditional Unionist Voice leader Jim Allister called on all members of the commission to resign.
"They're all culpable, and all of them, in consequence, must go," he said.
The DUP's Carla Lockhart has written to Collins after her interview on Good Morning Ulster, external and said: "Regrettably, you and your fellow Commissioners have lost the confidence of the entire unionist community. The interview this morning has only compounded matters."
First Minister Michelle O'Neill, who attended the Drumcree Community Centre on Wednesday and met residents said the community was "anxious by what they saw" on Tuesday.
She added that the "days of pushing any parades or any sort of negative experience again on any community here will not be acceptable or tolerated by anybody".
The current Commission was appointed from January 2024 on a three year term.
Professor Collins, a former chair of the Equality Commission, chairs a six-person panel. The others are Derek Wilson, a former banker, Billy Gamble, a former senior civil servant, Nicola Rountree, a barrister, Rachel Quigley, a solicitor and Pauline Leeson, a social worker.
According to the last annual report, the chair is paid between £50,000 and £55,000 while the other commissioners earn between £20,000 and £25,000.
The chair is expected to devote one to two days per week to the work of the Commission.
Commissioners are expected to devote approximately one day per week to commission business over the course of a year, with a proportionately greater commitment required April to August.
The member of the six-person commission who has faced the most public criticism is Billy Gamble.
He has been criticised over private comments he is alleged to have made about the Drumcree parade determination.
Collins said the comments were "out of line" but had no bearing on the decision-making process.
Asked if he should resign, the commission chair said: "That will be a matter for Billy Gamble."
